Question

How do you solve the following system?: `-8x+3y=12 , 8x-9y= 12`

Answer 1

`x=-3, y=-4`

Explanation:

Given: `8x-9y=12`. Solve for x.
`8x-9y+9y=12+9y`
`8x=12+9y`
`(8x)/8=(12+9y)/8`

`x=(12+9y)/8`

Substitute this into the other equation:

`-8x+3y=12`

`-8((12+9y)/8)+3y=12`

`-1(12+9y)+3y=12`

`-12-9y+3y=12`

`-12-6y=12`

`-12-6y+12=12+12`

`-6y=24`

`(-6y)/-6=24/-6`

`y=-4`

Substitute into original equation:

`8x-(9*-4)=12`

`8x+36=12`

`8x+36-36=12-36`

`8x =-24`

`(8x)/8=-24/8`

`x=-3`

To check, substitute both answers into both the formulas:

`-8*-3+3*-4=24-12=12` True

`8*-3-9*-4=-24+36=12` True