Question

Solve the following pair of simultaneous equations.

`7/x + 6/y = 71, 5/x - 8/y = -23`

Answer 1

Given equations:

`7/x + 6/y = 71`    ...(1)

`5/x - 8/y = -23`     ...(2)

Let, `a = 1/x, b = 1/y,`

Then the equations will become:

7a + 6b = 71    ...(1)

5a − 8b = −23     ...(2)

Here, multiplying equation (1) by 4:

4(7a) + 4(6b) = 4(71)

28a + 24b = 284     ...(3)

And, multiplying equation (2) by 3:

3(5a) − 3(8b) = 3(−23)

15a − 24b = −69     ...(4)

Now, adding equation (3) to equation (4):

(28a + 24b) + (15a − 24b) = 284 + (−69)

28a + 24b + 15a − 24b = 284 − 69

28a + 15a = 215

43a = 215

a = `215/43`

∴ a = 5

Let’s substitute a = 5 into equation (1):

7(5) + 6b = 71

35 + 6b = 71

6b = 71 − 35

6b = 36

b = `36/6`

∴ b = 6

Thus, finding x and y from `a = 1/x, b = 1/y,`

`a = 1/x = 5`

`∴ x = 1/5`

`b = 1/y = 6`

`∴ y = 1/6`