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

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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