{"id":33047,"date":"2019-04-12T15:31:00","date_gmt":"2019-04-12T10:01:00","guid":{"rendered":"https:\/\/www.cbselabs.com\/?p=33047"},"modified":"2021-09-18T15:21:34","modified_gmt":"2021-09-18T09:51:34","slug":"important-questions-for-cbse-class-9-mathematics-linear-equations-in-two-variables","status":"publish","type":"post","link":"https:\/\/www.cbselabs.com\/important-questions-for-cbse-class-9-mathematics-linear-equations-in-two-variables\/","title":{"rendered":"Important Questions for CBSE Class 9 Mathematics Linear Equations in Two Variables"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\">Important Questions for CBSE Class 9 Mathematics Chapter 1 Linear Equations in Two Variables<\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables:<\/p>\n<ul>\n<li>Linear Equations in Two Variables<\/li>\n<li>Introduction<\/li>\n<li>Linear Equations<\/li>\n<li>Solution Of A Linear Equation<\/li>\n<li>Graph Of A Linear Equation In Two Variables<\/li>\n<li>Equations Of Lines Parallel To The X-Axis And Y\u2013Axis<\/li>\n<li>Summary<\/li>\n<\/ul>\n<h3 style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>IMPORTANT QUESTIONS\u00a0<\/strong><\/span><\/h3>\n<p><span style=\"color: #0000ff;\"><strong>VERY SHORT ANSWER TYPE QUESTIONS<\/strong><\/span><br \/>\n<strong>Question.1 Linear equation x &#8211; 2 = 0 is parallel to which axis ? [CBSE-15-6DWMW5A]<\/strong><br \/>\n<strong> Solution.<\/strong> Here, linear equation is x-2 = 0\u00a0\u21d2 x = 2<br \/>\nThus, it is parallel to y-axis.<\/p>\n<p><strong>Question.2 If (1, -2) is a solution of the equation 2x &#8211; y = p, then find the value of p.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5669\/29600396984_7926e5cbcb_o.png?resize=414%2C95&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-1\" width=\"414\" height=\"95\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>More Resources for CBSE Class 9<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-2\/\">NCERT Solutions<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths\/\">NCERT Solutions Class 9 Maths<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-9-science\/\">NCERT Solutions Class 9 Science <\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-social-science\/\">NCERT Solutions Class 9 Social Science<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-9-english\/\">NCERT Solutions Class 9 English<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-9-hindi\/\">NCERT Solutions Class 9 Hindi<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-9th-sanskrit\/\">NCERT Solutions Class 9 Sanskrit<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-class-9-foundation-information-technology\/\">NCERT Solutions Class 9 IT<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/rd-sharma-class-9th-solutions\/\">RD Sharma Class 9 Solutions<\/a><\/li>\n<\/ul>\n<p><strong>Question.3 Express x\/4 &#8211; 3y = &#8211; 7 in the form of ax + by + c = 0. [CBSE-15-6DWMW5A]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5196\/29934311210_46106aa4df_o.png?resize=480%2C74&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-2\" width=\"480\" height=\"74\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question. 4 Find the value of k for which x = 0, y \u2014 8 is a solution of 3x &#8211; 6y = k.\u00a0<\/strong><strong>[CBSE-15-NS72LP7]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5494\/30195828616_62a8081b5e_o.png?resize=475%2C73&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-3\" width=\"475\" height=\"73\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question .5 Cost of a pen is two and half times the cost of a pencil. Express this situation as a<\/strong><br \/>\n<strong> linear equation in two variables. [CBSE-15-NS72LP7]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5785\/29934311070_d52735eb03_o.png?resize=417%2C136&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-4\" width=\"417\" height=\"136\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.6 Express x in term of y : x\/7 + 2y = 6 [CBSE-14-17DIG1U]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5074\/30195828486_3535a0e74f_o.png?resize=406%2C89&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-5\" width=\"406\" height=\"89\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.7 Find the two solutions of the linear equation 2x &#8211; 3y = 12.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5502\/29934311000_ecbf189df2_o.png?resize=499%2C153&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-6\" width=\"499\" height=\"153\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.8 If we multiply or divide both sides of a linear equation with a non-zero number, then what will happen to the solution of the linear equation ?\u00a0[NCERT Exemplar Problem]<\/strong><br \/>\n<strong> Solution.<\/strong> Solution remains the same.<\/p>\n<p><strong>Question. 9 How many linear equations in x and y can be satisfied by x = 1 and y = 2?\u00a0[NCERT Exemplar Problem]<\/strong><br \/>\n<strong> Solution.<\/strong> Infinitely many.<\/p>\n<p><strong>Question.10 In an one day international cricket match, Raina and Dhoni together scored 198 runs. Express the statement as a linear equation in two variables.\u00a0[CBSE-14-17DIG1U]<\/strong><br \/>\n<strong> Solution.<\/strong> Let runs scored by Raina be x and runs scored by Dhoni be y.<br \/>\nAccording to statement of the question, we have<br \/>\nx + y = 198<br \/>\nor x + y &#8211; 198 = 0<\/p>\n<p><strong>Question.11 Write the equation of a line which is parallel to x-axis and is at a distance of<\/strong><br \/>\n<strong> 2 units from the origin. [CBSE-14-ERFKZ8H<\/strong><br \/>\n<strong> Solution.<\/strong> Here, required line is parallel to x-axis and at a distance of 2 units from the origin.<br \/>\n.<sup>.<\/sup>. Its equation is<br \/>\ny + 2= 0 or y-2 = 0<\/p>\n<p><strong>Question.12 Find \u2018a\u2019, if linear equation 3x &#8211; ay = 6 has one solution as (4, 3).[CBSE -14- ERFKZ8H]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5828\/30195828406_01a28e1d00_o.png?resize=382%2C182&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-7\" width=\"382\" height=\"182\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.13 The cost of a notebook is Rs 5 less than twice the cost of a pen. Write this statement as a linear equation in two variables.<\/strong><br \/>\n<strong> Solution.<\/strong> Let Rs x be the cost of a notebook and Rs y be the cost of a pen, then, we have<br \/>\nx = 2y &#8211; 5<br \/>\n\u21d2 \u00a0 \u00a0 x &#8211; 2y + 5 = 0.<\/p>\n<p><strong>Question.14 Total cost of a laptop and a mobile phone is Rs 60000. Write a linear equation in two variables to represent this statement.<\/strong><br \/>\n<strong> Solution.<\/strong> Let the cost price of a laptop be Rs l and cost price of a mobile phone be Rs m.<br \/>\nSince combined cost of a laptop and a mobile phone is Rs 60000 So, l + m = 60000<\/p>\n<p><strong>Question.15 The cost of a table is Rs\u00a0100 more than half the cost of a chair. Write this statement as a linear equation in two variables.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8568\/29934310870_8c4a3b41df_o.png?resize=646%2C142&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-8\" width=\"646\" height=\"142\" data-recalc-dims=\"1\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>SHORT ANSWER QUESTIONS TYPE-I<\/strong><\/span><\/p>\n<p><strong>Question.16 In some countries temperature is measured in Fahrenheit, whereas in countries like India it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:<\/strong><br \/>\n<strong> F=[9\/5] c+32<\/strong><br \/>\n<strong> If the temperature is &#8211; 40\u00b0C, then what is the temperature in Fahrenheit ?[CBSE-14-GDQNI3 W]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/8\/7535\/30195828356_3eebcae0d7_o.png?resize=322%2C215&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-9\" width=\"322\" height=\"215\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.17 Write linear equation representing a line which is parallel to y-axis and is at a distance of 2 units on the left side of y-axis. [CBSE-14-GDQNI3W]<\/strong><br \/>\n<strong> Solution<\/strong>.Here, required equation is parallel to y-axis at a distance of 2 units on the left side of y-axis.<br \/>\nx = &#8211; 2 or x + 2 = 0<\/p>\n<p><strong>Question.18 Find the value ofk, if (1, -1) is a solution of the equation 3x-ky = 8. Also, find the coordinates of another point lying on its graph. [CBSE-15-NS72LP7]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5259\/29934310770_a8ee9a9f8c_o.png?resize=443%2C93&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-10\" width=\"443\" height=\"93\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8547\/30195828206_b78311ee50_o.png?resize=657%2C73&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-11\" width=\"657\" height=\"73\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.19 If (p, 2p + 1) is the solution of the linear equation 4x + 3y = 23. Find the value of p.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8747\/29934310620_d649ea3ea4_o.png?resize=632%2C105&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-12\" width=\"632\" height=\"105\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.20 Find the value of m, if (5,8) is a solution of the equation 11 x-2y = 3m, then find one\u00a0<\/strong><strong>more solution of this equation. [CBSE March 2013]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8140\/30195827996_2ceb34422e_o.png?resize=550%2C316&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-13\" width=\"550\" height=\"316\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.21 If \u03c0 x + 3y = 25, write y in terms of x and also, find the two solutions of this equation.\u00a0<\/strong><strong>[CBSE-14-17DIG1U]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<strong><img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5068\/29934310470_5881113db9_o.png?resize=554%2C267&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-14\" width=\"554\" height=\"267\" data-recalc-dims=\"1\" \/><\/strong><\/p>\n<p><strong>Question.22 Find four solutions of 2x-y = 4. [CBSE March 2011 ]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5074\/30195827796_8933e55fe2_o.png?resize=301%2C51&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables15\" width=\"301\" height=\"51\" data-recalc-dims=\"1\" \/><br \/>\n<strong><img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5204\/29600395684_d92a82a020_o.png?resize=692%2C185&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-16\" width=\"692\" height=\"185\" data-recalc-dims=\"1\" \/><\/strong><\/p>\n<p><strong>Question.23 Give equation of two lines on same plane which are intersecting at the point (2, 3).\u00a0<\/strong><strong>[CBSE March 2012]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\nSince there are infinite lines passing through the point (2, 3).<br \/>\nLet, first equation is x + y = 5 and second equation is 2x + 3y = 13<br \/>\nClearly, the lines represented by both equations intersect at the point (2, 3).<\/p>\n<p><strong>24. Let y varies directly as x. Ify = 12 when x = 4, then write a linear equation. What is\u00a0<\/strong><strong>the value of y,when x = 5 ? [NCERT Exemplar Problem]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c1.staticflickr.com\/9\/8626\/29600395584_f4929e94d2_o.png?resize=718%2C157&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-17\" width=\"718\" height=\"157\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.25 Give the equations of two lines passing through (2, 14). How many more such lines are there and why ?<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5350\/30195827706_5f1cdf8b12_o.png?resize=704%2C245&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-18\" width=\"704\" height=\"245\" data-recalc-dims=\"1\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>SHORT ANSWER QUESTIONS TYPE-II<\/strong><\/span><\/p>\n<p><strong>Question.26 Find the value of a for which the equation 2x + ay = 5 has (1, -1) as a solution. Find\u00a0<\/strong><strong>two more solutions for the equation obtained. [CBSE March 2011 ]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5643\/30145154941_7efacc1214_o.png?resize=409%2C108&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-19\" width=\"409\" height=\"108\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5282\/29600395114_84b5f8958b_o.png?resize=575%2C322&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-20\" width=\"575\" height=\"322\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.27 A fraction becomes 1\/4 when 2 is subtracted from the numerator and 3 is added to\u00a0the denominator. Represent this situation as a linear equation in two variables. Also, find two solutions for this. [CBSE-15-17DIG1U]<\/strong><br \/>\n<strong> Solution.<\/strong> Let numerator and denominator of the given fraction be respectively x and y. According to the statement, we obtain<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5671\/29600394934_1e0c288704_o.png?resize=411%2C231&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-21\" width=\"411\" height=\"231\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.28 Draw the graph of the linear equation y = 2\/3 x + 1\/3 . Check from the graph that \u00a0(7, 5)is a solution of the linear equation.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8694\/30145154731_5510a6f828_o.png?resize=636%2C212&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-22\" width=\"636\" height=\"212\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5302\/30230702205_7529bf1d1d_o.png?resize=713%2C367&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-23\" width=\"713\" height=\"367\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.29 The cost of two pizzas and 1 burger is Rs 450. Represent this situation algebraically and also, draw the graph. [CBSE-14-ERFKZ8H], [CBSE-15-6DWMW5A]<\/strong><br \/>\n<strong> Solution.<\/strong> Let cost price of one pizza be Rs x and that of one burger be Rs y.<br \/>\n.<sup>.<\/sup>. \u00a0According to given statement, we have<br \/>\n<strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02x + y = 450<\/strong><br \/>\n<strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u21d2 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = 450 &#8211; 2x<\/strong><br \/>\n<strong>\u00a0When x = 100, y = 250<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5724\/30230701965_c9e48b3bf0_o.png?resize=665%2C384&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-24\" width=\"665\" height=\"384\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.30 Express y in terms of x for the equation 3x &#8211; 4y + 7 = 0. Check whether the points (23, 4) and\u00a0<\/strong><strong>(0,7\/4)lie on the graph of this equation or not.<\/strong><br \/>\n<strong> Solution. <\/strong>Given equation is 3x &#8211; 4y + 7 = 0<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8560\/29600393534_d6b146bc9b_o.png?resize=714%2C548&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-25\" width=\"714\" height=\"548\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.31 The path of an aeroplane is given by the equation 3x &#8211; 4y = 12. Represent the graph graphically. Also, show that the point (- 4, &#8211; 6) lies on the graph.\u00a0[CBSE-15-NS72LP7]<\/strong><br \/>\n<strong> Solution.<\/strong> Given equation is 3x &#8211; 4y = 12<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5793\/30230701455_58350fda76_o.png?resize=296%2C219&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-26\" width=\"296\" height=\"219\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8587\/29600392914_e48e1cc338_o.png?resize=702%2C575&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-27\" width=\"702\" height=\"575\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.32 Rupinder and Deepak two students of a vidyalaya contribute to charity. The\u00a0Contribution of Rupinder is 2\/5 of the contribution of Deepak. Write a linear equation\u00a0According to the above statement and draw the graph for the linear equation.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5327\/29601244043_546090b6c1_o.png?resize=701%2C314&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-28\" width=\"701\" height=\"314\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.33 Draw the graph of the equation y = mx + c for m = 3 and c = &#8211; 1 (a straight line in Cartesian plane). Read from the graph the value of when x = 2.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5175\/29600392384_a060d35c36_o.png?resize=692%2C458&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-29\" width=\"692\" height=\"458\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.34 The following observed values of x Write the linear equation :<\/strong><br \/>\n<strong> Draw the graph using the values of x, graph of the linear equation.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5288\/29601243643_44e6fc941e_o.png?resize=185%2C71&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-30\" width=\"185\" height=\"71\" data-recalc-dims=\"1\" \/><br \/>\n<strong>(i) cuts the x-axis (ii) cuts the y-axis<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5216\/30230700995_023485a8a9_o.png?resize=740%2C328&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-31\" width=\"740\" height=\"328\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5656\/29600391694_76a639f3de_o.png?resize=734%2C328&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-32\" width=\"734\" height=\"328\" data-recalc-dims=\"1\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>LONG ANSWER TYPE QUESTIONS<\/strong><\/span><\/p>\n<p><strong>Question.35 On the graph paper draw the straight line 3x &#8211; 2y = 4 and x + y &#8211; 3 = 0. Also, find their point of intersection on the graph.<\/strong><br \/>\n<strong> Solution.<\/strong> The two given equations are<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5558\/30230700765_b24acc2c24_o.png?resize=709%2C517&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-33\" width=\"709\" height=\"517\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5189\/29600391344_8245fc4576_o.png?resize=730%2C458&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-34\" width=\"730\" height=\"458\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.36 If (2,3) and (4, 0) lie on the graph of equation ax + by = 1. Find the value of a and b. Plot the graph of equation obtained. [CBSE March 2012]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8729\/30230700405_81df923f7d_o.png?resize=729%2C495&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-35\" width=\"729\" height=\"495\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c1.staticflickr.com\/9\/8409\/29600390204_5388555170_o.png?resize=719%2C426&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-36\" width=\"719\" height=\"426\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.37 Draw the graphs of the following equations on the same graph sheet: x = 4,x = 2,y = l and y &#8211; 3 = 0<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5555\/30230699725_762966da95_o.png?resize=509%2C457&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-37\" width=\"509\" height=\"457\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.38 Write the equations of the lines drawn in following graph :<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8133\/29600389634_8672b15a54_o.png?resize=515%2C345&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-38\" width=\"515\" height=\"345\" data-recalc-dims=\"1\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8594\/30230699215_f9c50edcbb_o.png?resize=605%2C184&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-39\" width=\"605\" height=\"184\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.39 Represent 2x + 3y = 6 by a graph. Write the coordinates of the point where it meets:\u00a0<\/strong><strong>(a) x-axis (b) y-axis [CBSE-14-GDQNI3W]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8278\/29601241713_217f24a197_o.png?resize=712%2C421&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-40\" width=\"712\" height=\"421\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.40 You know that the force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation, taking constant as 5, force on y-axis and acceleration on x-axis. Also, find acceleration produced in a body, if force applied on it is 20 units. [CBSE-14-ERFKZ8H]<\/strong><br \/>\n<strong> Solution.<\/strong> Let x be the acceleration produced in the body on application of a force of y units. According to the statement of the question. We have y = kx, where k is a constant.<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8135\/30230698975_34b7687a7c_o.png?resize=643%2C546&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-41\" width=\"643\" height=\"546\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.41 Cost of 1 pen is Rs x and that of 1 pencil is Rs y. Cost of 2 pens and 3 pencils together is Rs 18. Write a linear equation which satisfies this data. Draw the graph for the same. [CBSE- 14ERFKZ8H]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c1.staticflickr.com\/9\/8127\/29601241403_024009e4ac_o.png?resize=364%2C110&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-42\" width=\"364\" height=\"110\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5501\/30115734052_d7fcd4606a_o.png?resize=561%2C491&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-43\" width=\"561\" height=\"491\" data-recalc-dims=\"1\" \/><br \/>\nPlot the points (0, 6), (3, 4) and (9, 0). Join them in pairs to get the required line.<\/p>\n<p><strong>Question.42 Sum of two numbers is 8. Write this in the form of a linear equation in two variables. Also, draw the line given by this equation. Find graphically the numbers, if difference between them is 2. [CBSE-15-6DWMW5A]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/6\/5290\/30230698365_14b1628d63_o.png?resize=278%2C229&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-44\" width=\"278\" height=\"229\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5724\/30115733712_b3bbe9a57b_o.png?resize=617%2C358&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-45\" width=\"617\" height=\"358\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8275\/30230697765_87eec122be_o.png?resize=662%2C504&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-46\" width=\"662\" height=\"504\" data-recalc-dims=\"1\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Value Based Questions (Solved)<\/strong><\/span><br \/>\n<strong>Question.1 If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also, read from the graph the work done when the distance travelled by the body is :<\/strong><br \/>\n<strong> (i) 2 units (ii) 0 unit.<\/strong><br \/>\n<strong> (iii) In context of values, if work done relates with \u2018Hard work\u2019 and \u2018Knowledge\u2019 relates with \u2018key\u2019 then what will one achieve ?<\/strong><br \/>\n<strong> Solution.<\/strong> Let the work done by constant force be y units and the distance travelled by the body be x units.\u00a0Since the work done by a body on application of a constant force (F) is directly proportional to the distance travelled by the body.<br \/>\nIt can be expressed in the form of a linear equation in two variables is as<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c2.staticflickr.com\/8\/7461\/30115732872_cc806a155b_o.png?resize=779%2C428&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-47\" width=\"779\" height=\"428\" data-recalc-dims=\"1\" \/><br \/>\nNow, we have to draw the graph by taking the constant force as 5 units.<br \/>\nFrom equation (i), we have<br \/>\nFrom graph:<\/p>\n<ol>\n<li>\u00a0When the distance travelled is 2 units, then the work done is 10 units.<\/li>\n<li>When the distance travelled is 0 unit, then the work done is also 0 unit.<\/li>\n<li>Success<\/li>\n<\/ol>\n<p><strong>Question.2 Lipsa and Mona are two students of IX class of DAV school. Together they contributed? 100 towards the old age home to help the old persons.<\/strong><br \/>\n<strong> (i) Write a linear equation which satisfies the given data and draw the graph.<\/strong><br \/>\n<strong> (ii)What values are depicted in their plan?<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5341\/30230697055_752544063b_o.png?resize=693%2C115&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-48\" width=\"693\" height=\"115\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i1.wp.com\/c1.staticflickr.com\/9\/8418\/30195829516_bd431d3d6b_o.png?resize=658%2C159&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-49\" width=\"658\" height=\"159\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5332\/29934311990_dc29628116_o.png?resize=609%2C425&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-50\" width=\"609\" height=\"425\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.3 Mrs Sharma lost her purse containing 50 rupee and 100 rupee notes amount to Rs 1500 in a shop. Next day shopkeeper found the purse during dusting. He immediately went to Mrs Sharma\u2019s house and returned the purse and rupees. Mrs Sharma appreciates the shopkeeper for his act. \u2018<\/strong><br \/>\n<strong> (i) Represent the situation as an equation and draw the graph.<\/strong><br \/>\n<strong> (ii)What value do you learn from shopkeeper\u2019s act ?<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5603\/30195829266_7c79d2d54d_o.png?resize=699%2C329&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-51\" width=\"699\" height=\"329\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i0.wp.com\/c2.staticflickr.com\/6\/5836\/29934311770_0449553fa7_o.png?resize=676%2C193&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-52\" width=\"676\" height=\"193\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c1.staticflickr.com\/9\/8139\/30195829256_0428b55c18_o.png?resize=587%2C450&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-53\" width=\"587\" height=\"450\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question.4 In an election, a good candidate may lose because 40% of voters do not cast their votes due to various reasons. Form an equation and draw the graph with data. From the graph, find:<\/strong><br \/>\n<strong> (i) The total number of voters, if 720 voters cast their votes.<\/strong><br \/>\n<strong> (ii)The number of votes cast, if the total number of voters are 1000.<\/strong><br \/>\n<strong> (iii) What message did you get from above information?<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c1.staticflickr.com\/9\/8575\/29600397534_3f60b424bc_o.png?resize=740%2C265&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-54\" width=\"740\" height=\"265\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/i2.wp.com\/c2.staticflickr.com\/6\/5564\/30195829006_737d495483_o.png?resize=741%2C531&#038;ssl=1\" alt=\"important-questions-for-cbse-class-9-mathamatics-linear-equations-in-two-variables-55\" width=\"741\" height=\"531\" data-recalc-dims=\"1\" \/><br \/>\nFrom the graph, we see that:<br \/>\n(i) When total votes polled = 720 i.e., y = 720, the total number of voters i.e., x = 1200 Hence, total number of voters = 1200.<br \/>\n(ii)When total number of voters x = 1000 Number of votes cast is 600.<br \/>\n(iii) Every voters should cast vote to elect an honest candidate.<\/p>\n<div class=\"featured-snippet\">\n<h2>NCERT Solutions for Class 9 Maths<\/h2>\n<ol>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-number-system\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 1 Number systems<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-2-polynomials\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 2 Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-3-coordinate-geometry\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 3 Coordinate Geometry<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-linear-equations-in-two-variables\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 4 Linear Equations in Two Variables<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-5-introduction-to-euclid-geometry\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 5 Introduction to Euclid Geometry<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-6-lines-and-angles\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 6 Lines and Angles<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-7-triangles\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 7 Triangles<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-8-quadrilaterals\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 8 Quadrilaterals<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-areas-of-parallelograms-and-triangles\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 9 Areas of Parallelograms and Triangles<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-10-circles\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 10 Circles<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-11-constructions\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 11 Constructions<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-12-herons-formula\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 12 Heron\u2019s Formula<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-13-surface-areas-and-volumes\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 13 Surface Areas and Volumes<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-14-statistics\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 14 Statistics<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-9-maths-chapter-15-probability\/\" target=\"_blank\" rel=\"noopener noreferrer\">Chapter 15 Probability<\/a><\/li>\n<li><a href=\"https:\/\/www.cbselabs.com\/wp-content\/uploads\/2016\/02\/NCERTSolutionsForClass9Maths.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Class 9 Maths (Download PDF)<\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Important Questions for CBSE Class 9 Mathematics Chapter 1 Linear Equations in Two Variables NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables: Linear Equations in Two Variables Introduction Linear Equations Solution Of A Linear Equation Graph Of A Linear Equation In Two Variables Equations Of Lines Parallel To The X-Axis &hellip;<\/p>\n","protected":false},"author":27,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.2 (Yoast SEO v17.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Important Questions for CBSE Class 9 Mathematics Linear Equations in Two Variables - CBSE Labs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.cbselabs.com\/important-questions-for-cbse-class-9-mathematics-linear-equations-in-two-variables\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Important Questions for CBSE Class 9 Mathematics Linear Equations in Two Variables\" \/>\n<meta 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