Question

How do you solve `3x+6y=-6` and `-7x+y=29` using substitution?

Answer 1

`(x,y)=(-4,1)`

Explanation:

Solve one of these equations for `y` to make substitution possible. The second equation appears best suited for this:

`-7x+y=29`

`y=7x+29`

We can now replace all instances of `y` in the first equation with `7x+29:`

`3x+6(7x+29)=-6`

`3x+42x+174=-6`

`45x=-6-174`

`45x=-180`

`x=-180/45`

`x=-4`

To find `y,` plug in the result above into either of the two equations. We solved the second one for `y,` so that will be the easiest one to use:

`y=7(-4)+29`

`y=1`