#### Can the following equations hold simultaneously?

3x – 7y = 7

11x + 5y = 87

5x + 4y = 43.

If so, find x and y.

**Solution:**

3x – 7y = 7 …… (1)

11x + 5y = 87 ….. (2)

5x + 4y = 43 ….. (3)

Now multiply equation (1) by 5 and (2) by 7

15x – 35y = 35

77x + 35y = 609

By adding both the equations

92x = 644

By division

x = 644/92 = 7

Substitute the value of x in equation (1)

3 × 7 – 7y = 7

By further calculation

21 – 7y = 7

So we get

– 7y = 7 – 21 = – 14

y = – 14/ – 7 = 2

Therefore, x = 7 and y = 2.

If x = 7 and y – 2 satisfy the equation (3) then we can say that the equations hold simultaneously

Substitute the value of x and y in equation (3)

5x + 4y = 43

By further calculation

5 × 7 + 4 × 2 = 43

So we get

35 + 8 = 43

43 = 43 which is true.

Therefore, the equations hold simultaneously.

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