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Example 5 - Graphically find whether no solution, unique

Example 5 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Example 5 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3
Example 5 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4

 

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Example 5 Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: 5x – 8y + 1 = 0 & 3x – 24/5 y + 3/5 = 0 Given equations are 5x − 8y + 1 = 0 3x – 24/5 y + 3/5 = 0 Simplifying them 5x − 8y = −1 15x – 24y = −3 For Equation (1) 5x − 8y = −1 Putting x = 0 5(0) − 8y = −1 0 − 8y = −1 y = (−1)/(−8) y = 0.125 So, x = 0, y = 0.125 is a solution i.e. (0, 0.125) is a solution Putting x = −1 5(−1) − 8y = −1 −5 − 8y = −1 −8y = −1 + 5 y = 4/(−8) y = −0.5 So, x = −1, y = −0.5 is a solution i.e. (−1, −0.5) is a solution For Equation (2) 15x – 24y = −3 Putting x = 0 15(0) − 24y = −3 0 − 24y = −3 y = (−3)/(−24) y = 0.125 So, x = 0, y = 0.125 is a solution i.e. (0, 0.125) is a solution Putting x = −1 15(−1) − 24y = −3 −15 − 24y = −3 −24y = −3 + 15 y = 12/(−24) y = −0.5 So, x = −1, y = −0.5 is a solution i.e. (−1, −0.5) is a solution We will plot both equations on the graph Since the lines are coincident, the given equations have infinitely many solutions

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.