Question

How do you solve `x = -5 + 2y` and `2x + 3y = 4` using substitution?

Answer 1

To solve, substitute the `x` in the second equation for the `x` in the first equation.

Explanation:

The first equation is already solved for `x`, so let's put that equation into the second equation. It'll look like this:

`2(-5+2y)+3y=4`

Next, use the distributive property to simplify our equation:

`-10+4y+3y=4`

Now, let's combine `3y` and `4y` to make `7y`:

`-10+7y=4`

Next, add `10` to each side:

`7y=14`

The final step in solving for y is to divide each side by `7`:

`y=2`

We've now solved for y. Now, we have to solve for x. The easiest way to do this is to substitute our y-value into the first equation, since it's already solved for x:

`x=-5+2(2)`

`x=-5+4`

`x=-1`

Using our x and y value and combining them to get an ordered pair, we now have our answer: `(-1,2)`