Question

How do you solve `2x + y = 1` and `4x + 2y = -2` using substitution?

Answer 1

Solve the first equation for `y` and put it into the second equation.

Explanation:

We're going to have to plug one equation into the other if we want to solve for `x` and `y`. First, we'll take the first equation and subtract `2x` from each side so that the equation is written in terms of `y`:

`y=-2x+1`

Next, we substitute the `y` in the second equation with the first equation and solve for `x`:

`4x+2(2x+1)=-2`
`4x+4x+2=-2`
`8x+2=-2`
`8x=-4`
`x=-1/2`

To solve for `y`, let's take our first equation and plug in our answer for `x`:

`y=-2(-1/2)+1`
`y=1+1`
`y=2`