Question

How do you solve the following system using substitution?: `-2x+5y=-2, x-3y=3`

Answer 1

Re-write one of the equations into the form
`color(white)("XXX")x= "an expression"`
then substitute the "expression" for `x` in the other equation.
`color(white)("XXX")(x,y)=(-9,-4)`

Explanation:

Given
[1]`color(white)("XXX")-2x+5y=-2`
[2]`color(white)("XXX")x-3y=3`

Rearranging the terms of [2]
[3]`color(white)("XXX")x=3y+3`

Substituting `3y+3` for `x` in [1]
[4]`color(white)("XXX")-2(3y+3)+5y = -2`

Simplifying
[5]`color(white)("XXX")-6y-6+5y=-2`

[6]`color(white)("XXX")y=-4`

Substituting `(-4)` for `y` in [2]
[7]`color(white)("XXX")x-3(-4)=3`

[8]`color(white)("XXX")x=-9`