Question

How do you solve the following system?: `-9x -8y =-3, 2x -2y = -4`

Answer 1

The solution for the system of equations is:
`color(green)(x = -13 / (17)`

`color(green)(y =21/17`

Explanation:

`-9x-color(blue)(8y)=-3`.......equation `(1)`

`2x-2y = -4`, multiplying this equation by `4`
`8x-color(blue)(8y) = -16`..........equation `(2)`

Solving by elimination

Subtracting equation `2` from `1`:

`-9x-cancelcolor(blue)(8y)=-3`
`-8x +cancelcolor(blue)(8y) = 16`

`-17x = 13`

`color(green)(x = -13 / (17)`

Finding `y` from equation `1`

`-9x-color(blue)(8y)=-3`

`-9x+ 3 = 8y`

`-9 xx color(green)( -13 / (17))+ 3 = 8y`

`117 / (17)+ 3 = 8y`

`117 / (17)+ 51/17 = 8y`

`168/17 = 8y`

`y =168/(17 xx 8)`

`color(green)(y =21/17`