Question

How do you solve the system of equations: `8x + 5y = - 17;- 3x - 8y = - 12`?

Answer 1

x=-4 and y=3

Explanation:

When you multiply the first equation by 3 and the second equation by 8, you get:

`24x+15y=-51` and
`-24x-64y=-96`.

Combine these two. Get:
`-49y=-147`
Then you will get `y=3`.

Since `8x+5y=-17`, this equation becomes
`8x+5*3=-17` or `8x=-32`.

`x=-4` is the answer.

Answer 2

`x=-4` and `y=3`

Explanation:

`8x+5y=-17` `color(white)(/////)`⟶ ①
`-3x-8y=-12` `color(white)(....)`⟶ ②

From ②,

`-3x-8y=-12`
`color(white)(i.)3x+8y=12`
`color(white)(xxxxx)3x=12-8y`
`color(white)(xxxxx.)x=(12-8y)/3` ⟶ ③

Substitute ③ into ①,

`color(white)(xxxxxx..x)8x+5y=-17`
`8((cancel(12_4)-8y)/3)+5y=-17`
`color(white)(x..)8(4-(8y)/3)+5y=-17`
`color(white)(xxxx)32-(64y)/3+5y=-17`
`color(white)(xxxxxx/..)(64y)/3-5y=32+17`
`color(white)(xxxxxxxx.x)(cancel(49_1)y)/3=cancel(49_1)`
`color(white)(xxxxxxxxxxxxx)y=3`

When `y=3` from ①,

`color(white)(//)8x+5y=-17`
`8x+5(3)=-17`
`color(white)(/)8x+15=-17`
`color(white)(xxxx.)8x=-32`
`color(white)(xxxxx.)x=-4`

Hence, `x=-4` and `y=3`.