Question

How do you solve the system `y=5x-7` and `-3x-2y=-12` by substitution?

Answer 1

We know that `y=5x-7` so we are just going to replace the `y` in the other equation :

`-3x-2y=-12`
`-3x-2*(5x-7)=-12`
`-3x-10x+14=-12`
`-13x=-12-14` ( we substract `14` on each side )
`-13x=-26`
`x=2` ( we divide by `-13` on each side )

Now that we have `x`, we can find `y` with the first equation :

`y=5x-7`
`y=5*2-7`
`y=10-7`
`y=3`