Let's work to solve this system of equations:

The tricky thing is that there are two variables, $x$ and $y$. If only we could get rid of one of the variables...

Here's an idea! Equation $1$ tells us that $\goldD{2x}$ and $\goldD y$ are equal. So let's plug in $\goldD{2x}$ for $\goldD y$ in Equation $2$ to get rid of the $y$ variable in that equation:

Brilliant! Now we have an equation with just the $x$ variable that we know how to solve:

Nice! So we know that $x$ equals $8$. But remember that we are looking for an ordered pair. We need a $y$ value as well. Let's use the first equation to find $y$ when $x$ equals $8$:

Sweet! So the solution to the system of equations is $(\blueD8, \greenD{16})$. It's always a good idea to check the solution back in the original equations just to be sure.

Let's check the first equation:

Let's check the second equation:

Great! $(\blueD8, \greenD{16})$ is indeed a solution. We must not have made any mistakes.

Your turn to solve a system of equations using substitution.

## Solving for a variable first, then using substitution

Sometimes using substitution is a little bit trickier. Here's another system of equations:

Notice that neither of these equations are already solved for $x$ or $y$. As a result, the first step is to solve for $x$ or $y$ first. Here's how it goes:

**Step 1: Solve one of the equations for one of the variables.**

Let's solve the first equation for $y$:

**Step 2: Substitute that equation into the other equation, and solve for $x$.**

**Step 3: Substitute $x = 4$ into one of the original equations, and solve for $y$.**

So our solution is $(\blueD4, \greenD 3)$.