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Solve the following equations by the reduction method. 5x + 2y = 4, 7x + 3y = 5 - Mathematics and Statistics

Sum

Solve the following equations by the reduction method.

5x + 2y = 4, 7x + 3y = 5

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Solution

5x + 2y = 4 ...............(1)

7x + 3y = 5 ...............(2)

Multiplying Eq. (1) with 7 and Eq. (2) with 5

35x + 14 y = 28
35x + 15 y = 25
      −        −        
      − 1y = 3
            y = − 3

Put y = − 3 into Eq. (1)
5x + 2y = 4
5x + 2(− 3) = 4
5x − 6 = 4
5x = 4 + 6
5x = 10
x = `10/5`
x = 2

Hence, x = 2, y = − 3 is the required solution.

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