Question

How do you solve the following system using substitution?: `-3x + 3y= 3, -5x + y = 13`

Answer 1

`x=-3`
`y=-2`

Explanation:

First, isolate `y` in the first equation.

`color(blue)([1])" "-3x+3y=3`

`color(blue)([2])" "3y=3+3x`

`color(blue)([3])" "y=1+x`

Now substitute the value of `y` in the first equation to `y` in the second equation.

`color(red)([1])" "-5x+color(blue)(y)=13`

`color(red)([2])" "-5x+color(blue)((1+x))=13`

`color(red)([3])" "-4x=12`

`color(red)([4])" "x=-3`

Now that we have the value of `x`, we will simply substitute this to the first equation.

`color(blue)([4])" "y=1+(-3)`

`color(blue)([5])" "y=-2`