Question

How do you solve this system of equations: `-4x - 2y = - 12; 4x + 8y = 24`?

Answer 1

`x=2` and `y=2`

Explanation:

`-4x-2y=-12`
`4x+8y=24`

We first simplify the two equations:

A] `-4x-2y=-12`

Divide all terms by `2`.

`-2x-y=-6`

Multiply all terms by `-1`.

`2x+y=6`

Subtract `y` from each side.

`2x=6-y`

B] `4x+8y=24`

Divide all terms by `2`.

`2x+4y=12`

In this equation, substitute `2x` with `color(red)((6-y))` derived from the first equation.

`2x+4y=12`

`color(red)((6-y))+4y=12`

Open the brackets and simplify.

`color(red)(6-y)+4y=12`

`6+3y=12`

Subtract `6` from each side.

`3y=6`

Divide both sides by `3`.

`y=2`

In the second equation, substitute `y` with `color(blue)(2)`.

`4x+8y=24`

`4x+8color(blue)((2))=24`

Open the brackets and simplify.

`4x+16=24`

Subtract `16` from each side.

`4x=8`

Divide both sides by `4`.

`x=2`