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

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Example 4 Check graphically, whether the pair of equations x + 3y = 6 and 2x – 3y= 12 is consistent. If so, solve them graphically. Let equations be x + 3y = 6 2x – 3y = 12 Let’s draw their graphs For Equation (1) x + 3y = 6 Putting x = 0 0 + 3y = 6 3y = 6 y = 6/3 y = 2 So, x = 0, y = 2 is a solution i.e. (0, 2) is a solution Putting y = 0 x + 3(0) = 6 x + 0 = 6 x = 6 So, x = 6, y = 0 is a solution i.e. (6, 0) is a solution For Equation (2) 2x − 3y = 12 Putting x = 0 2(0) − 3y = 12 0 − 3y = 12 −3y = 12 y = 12/(−3) y = −4 So, x = 0, y = −4 is a solution i.e. (0, −4) is a solution Putting y = 0 2x − 3(0) = 12 2x = 12 x = 12/2 x = 6 So, x = 6, y = 0 is a solution i.e. (6, 0) is a solution We will plot both equations on the graph Since the lines intersect, the given equations are consistent And solution is (6, 0)