Question

How do you solve the system `2x-3y=12 and x=4y+1`?

Answer 1

`x = 9`
`y = 2`

Explanation:

`2x - 3y = 12`
`x = 4y + 1`

Solving by Substitution

First, we're going to use an equation for the value of a variable in order to plug it into the opposite equation of the system. Because `x = 4y + 1` is already an equation for the value of a variable, we'll be using it. In the other equation of the system, plug in `x`'s value where `x` is. So:

`2(4y + 1) - 3y = 12`

Next, you'll be distributing. What this means is that you'll be multiplying the outside number, `2`, by the terms in the parentheses, `4y` and `1`. So:

`2 * 4y = 8y`
`2 * 1 = 2`

Re-write your equation.

`8y + 2 - 3y = 12`

Combine like terms. `8y - 3y = 5y`, so:

`5y + 2 = 12`

This is a two-step equation. To solve it, subtract 2 from both sides to isolate for `y`. You should now have:

`5y = 10`

Divide by `5` to isolate for `y`:

`y = 2`

Plug the value of `y` back into the equation for the value of `x`:

`x = 4y + 1`
`x = 4(2) + 1`
`x = 8 + 1`
`x = 9`

To truly prove that `x` is 9 and `y` is 2:

`2x - 3y = 12`
`2(9) - 3(2) = 12`
`18 - 6 = 12`
`12 = 12`