Question

What is the solution to the system of equations: `6=-4x+y, -5x-y=21`?

Answer 1

`x=-3` and `y=-6`

Explanation:

1. `6=-4x+y`
2. `-5x-y=21`

From the first equation we can determine a value for `y`.

`6=-4x+y`

Add `4x` to both sides.

`4x+6=y`

In the second equation, substitute `y` with `color(red)((4x+6))`.

`-5x-color(red)((4x+6))=21`

Open the brackets and simplify. The multiplication of a negative and a positive results in a negative.

`-5x-color(red)(4x-6)=21`

`-9x-6=21`

Add `6` to both sides.

`-9x=27`

Divide both sides by `9`.

`-x=3` or `x=-3`

In the first equation, substitute `x` with `-3`.

`6=-4(-3)+y`

Open the brackets. The multiplication of two negatives results in a positive.

`6=12+y`

Subtract `12` from both sides.

`-6=y` or `y=-6`