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 – 24/5y + 3/5 = 0 5x − 8y + 1 = 0 3x – 24/5 y + 3/5 = 0 Solving (1) 5x − 8y + 1 = 0 8y = 5x + 1 y = (5𝑥 + 1)/8 Let x = 3, y = (5(3) +1)/8 y = (15 + 1)/8 y = 16/8 y = 2 So, x = 3, y = 2 is a solution ,i.e., (3,2) is a solution. Let x = 0, y = (5(0) +1)/8 y = (0 + 1)/8 y = 1/8 y = 0.125 So, x = 0, y = 0.125 is a solution ,i.e., (0,0.125) is a solution. Solving (2) 3x − 24/5 y + 3/5 = 0 24/5 y = 3x + 3/5 24/5 𝑦 = (3𝑥 × (5)+ 3)/5 24𝑦 = 15𝑥 + 3 y = (15𝑥 + 3)/24 Let x = 0, y = (15(0) + 3)/24 = 3/24 = 1/8 = 0.125 So, x = 0, y = 0.125 is a solution ,i.e., (0,0.125) is a solution Let x = -1 y = (15(−1) + 3)/24 = (−15 + 3)/24 = (−12)/24 = −1/2 = − 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 So, the pair of equations have infinitely many solutions