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Question

# Question 1 (ii) Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x - 2y = 2

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Solution

## 3x + 4y = 10 and 2x - 2y = 2 By elimination method: 3x + 4y = 10 .... (i) 2x - 2y = 2 ... (ii) Multiplying equation (ii) by 2, we get 4x - 4y = 4 ... (iii) 3x + 4y = 10 ... (i) Adding equation (i) and (iii), we get 7x + 0 = 14 Dividing both side by 7, we get x=147=2 Putting in equation (i), we get 3x + 4y = 10 3(2) + 4y = 10 6 + 4y = 10 4y = 10 - 6 4y = 4 y=44=1 Hence, answer is x = 2, y = 1 By substitution method: 3x + 4y = 10 ... (i) Subtract 3x both side, we get 4y = 10 - 3x Divide by 4 we get y=(10−3x)4 Putting this value in equation (ii), we get 2x - 2y = 2 ... (ii) 2x−2(10−3x)4=2 Multiply by 4 we get 8x - 2(10 - 3x) = 8 8x - 20 + 6x = 8 14x = 28 x=2814=2 y=10−3x4 y=44=1 Hence, answer is x = 2, y = 1 again.

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