Question

How do you solve the system of equations `x- 9y = 20` and `10x - 18y = - 16`?

Answer 1

Please see the explanation. `x = -7 and y = -3`

Explanation:

Given:

`x - 9y = 20` [1]
`10x - 18y = -16` [2]

Multiply equation [1] by -2 and add to equation 2:

`10x - 2x - 18y + 18y = -16 - 40`

`8x = -56`

`x = -7`

Substitute -7 for x into equation [1]

`-7 - 9y = 20`

`-9y = 27`

`y = -3`

Check:

`-7 - 9(-3) = 20`
`10(-7) - 18(-3) = -16`

`20 = 20`
`-16 = -16`

This checks