Question

How do you solve the following system?: `2x +y = 13 , 3x +2y = -2`

Answer 1

`(x,y)=(28,-43)`

Explanation:

Given:
[1]`color(white)("XXX")2x+y=13`
[2]`color(white)("XXX")3x+2y=-2`

Multiply [1] by `2` to give `y` a coefficient equal to that in [2]
[3]`color(white)("XXX")4x+2y=26`

Subtract [2] from [3] to eliminate the `y` term
[4]`color(white)("XXX")x=28`

Substitute `28` for `x` back into [1]
[5]`color(white)("XXX")2xx28 +y=13`

Simplify
[6]`color(white)("XXX")y=13-56 = -43`

Answer 2

`x=28`
`y=-43`

Explanation:

Given -

`2x+y=13` ---------------------------(1)
`3x+2y=-2` ---------------------------(2)

Solve equation (1) for `y`

`y=13-2x`

Substitute `y=13-2x` in equation (2)

`3x +2(13-2x)=-2`
`3x+26-4x=-2`
`-x+26=-2`
`-x=-2-26`
`-x=-28`
`x=28`

Substitute `x=28` in equation (1)

`2(28)+y=13`
`56+y=13`
`y=13-56=-43`
`y=-43`