Question

How do you solve `5x - y = -9` and `y + 2x = 2`?

Answer 1

The solution is `(-11/3,28/3)` or `~~(-3.67,9.33)`.

Explanation:

Solve the linear system:

`"Equation 1":` `5x-y=-9`

`"Equation 2":` `y+2x=2`

I am going to solve the system by elimination and substitution.

Rearrange Equation 2 to standard form: `Ax+By=C`

`2x-y=2`

Multiply Equation 2 by `-1`. This will reverse the signs, but the graph will remain the same.

`-1(2x-y)=2xx-1`

`-2x+y=-2`

Add Equation 1 and Equation 2.

`color(white)(..)5x-y=-9`
`-2x+y=-2`
`-------`
`color(white)(..)3xcolor(white)(.....)=-11`

Divide both sides by `3`.

`x=-11/3` or `~~-3.67`

Substitute `-11/3` for `x` in Equation 2 and solve for `y`.

`2(-11/3)+y=2`

`-22/3+y=2`

Multiply both sides by `3`.

`-22+3y=6`

Add `22` to both sides.

`3y=6+22`

Simplify `6+22` to `28`.

`3y=28`

Divide both sides by `3`.

`y=28/3` or `~~9.33`

graph{(5x-y+9)(-2x+y+2)=0 [-12.795, 9.705, -15.865, -4.615]}