Question

Solve the following pair of simultaneous equations.

`15/x + 4/y = 7, 9/x - 8/y = -1`

Answer 1

Given equations:

`15/x + 4/y = 7`    ...(1)

`9/x - 8/y = -1`    ...(2)

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

Then the equations will become:

15a + 4b = 7    ...(1)

9a − 8b = −1     ...(2)

Here, multiplying equation (1) by 2:

2(15a) + 2(4b) = 2(7)

30a + 8b = 14     ...(3)

Now, adding equation (2) to equation (3):

(30a + 8b) + (9a − 8b) = 14 + (−1)

30a + 8b + 9a − 8b = 14 − 1

30a + 9a = 13

39a = 13

a = `(13)/39`

∴ a = `1/3`

Let’s substitute `a = 1/3` into equation (1):

`15(1/3) + 4b = 7`

`(15)/3 + 4b = 7`

5 + 4b = 7

4b = 7 − 5

4b = 2

b = `2/4`

∴ b = `1/2`

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

`a = 1/x = 1/3`

∴ x = 3

`b = 1/y = 1/2`

∴ y = 2