Question

How do you solve the system of equations `y=-x-4` and `y=x+2`?

Answer 1

`x = -3` and `y = -1`.

Explanation:

`y = -x-4`
`y = x + 2`
Substituting `-x-4` for `y`:
`-x-4=x+2`
`2x = -6`
`x=-6/2`
`x=-3`
Substituting -3 for x to find y:
`y = 3 -4`
`y=-1`

Answer 2

`x = -3`
`y = -1`

Explanation:

Since both equations are set in terms of y (y equals), we can set both equations equal to each other:

`-x-4=x+2`

From here we can solve a very simple equation:

`-x-x=-2x` (Get like terms on both sides, x's on the left, coefficients on the right)
`4+2=6`
`-2x=6`
`x=-3`

Now that we have x, we can choose one of either equations to solve for y, and plug both values in after to double check:

`y=-(-3)-4`
`y=3-4`
`y=-1`

Let's double check by using the other equation:

`y=x+2`
`(-1)=(-3)+2`
`-1=-1`,
True