Question

How do you solve the following system?: `x - y = -6, 3x+2y=12`

Answer 1

The solution for the system of equations is
`color(blue)(x=0,y=6`

Explanation:

`x-y=-6`, multiplying this equation by `3`
`color(blue)(3x)-3y=-18`.......equation `(1)`

`color(blue)(3x) +2y=12`..............equation `(2)`

Solving by elimination.

Subtracting equation `2` from `1`:

`cancelcolor(blue)(3x)-3y=-18`
`cancel(-color(blue)(3x)) -2y=-12`

`-5y=-30`

`y=30/5`

`color(blue)(y=6`

Finding `x` by substituting `y` in equation `1`

`x-y=-6`

`x=-6 +y`

`x=-6 +6`

`color(blue)(x=0`