Question

How do you solve `2x-y=6` and `x+y=-3`?

Answer 1

`x=1`
`y=-4`

Explanation:

There are 3 ways to solve this. Here is one way:

Elimination:

Line them up:

`2x-y=6`
`x+y=-3`

Add all that goes together:

`2x+x=3x`
`-y+y=0`
`6-3=3`

Put it back into an equation:

`3x=3`

`x=1`

Plug what x equals (1) into one of the previous equations:

`(2•1)-y=6`
`(-2)-y=6-2`
`-y=4 or y=-4`

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

Answer 2

`x=1`

`y=-4`

Explanation:

These are called simultaneous equations. Multiply both equations so they both have the same leading coefficient. Use the coefficient of `x` in one equation to multiply the entire equation of the other one. Do this for both.

`[2x-y=6]" " xx1`
`[x+y=-3]" " xx2`

Equals

`2x-y=6`
`2x+2y=-6`

Then subtract the two equations

`2x-2x=0`
`[-y]-[2y]=-3y`
`6-[-6]=12`

Result:

`-3y=12`

Simplify:

`-y=4`

so

`y=-4`

Replace the `y` in one of the equations with `-4` to solve for `x`.

`2x-y=6`

`2x- (-4)=6`

`2x+4=6`

`2x=6-4`

`2x=2`

`x=1`