Example 7 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Important Question)

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Example 7 Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the rails cross each other? Given equations are x + 2y = 4 2x + 4y = 12 We need to check if the rails cross each other i.e. if both equations form a unique solution From (1) x + 2y – 4 = 0 x = 4 – 2y Substitute the value of x in equation (2) 2x + 4y – 12 = 0 2 (4 – 2y) + 4y – 12 = 0 8 – 4y + 4y – 12 = 0 −4 = 0 Which is not correct Thus, The Given equations do not have a solution So , the two rails will not cross each other.