Question

How do you solve by substitution `-x + 2y = -6` and `3x + y = 8`?

Answer 1

`(22/7,-10/7)`

Explanation:

In the second equation, we can easily solve for `y` by subtracting `3x` from both sides. We get:

`y=8-3x`

We've already solved for one variable in terms of the other, so we can plug into the first equation. We get

`-x+2(8-3x)=-6`

`=>-x+16-6x=-6`

`=>-7x+16=-6`

We can subtract `16` from both sides to get

`-7x=-22`

Dividing both sides by `-7`, we get

`color(blue)(x=22/7)`

We can plug into our equation for `y`, `y=8-3x`. We get

`y=8-3(22/7)`

`y=56/7-66/7`

`color(lime)(y=-10/7)`

Hope this helps!