# What is the solution to the system of equations x=y-3, x+3y=13?

Dec 20, 2016

$x = 1 , y = 4$.

#### Explanation:

Here's one of many ways of solving this system. Since we are already told that $x = y - 3$ from the first equation, just plug in $y - 3$ everywhere you see an $x$ in the second equation.

So the second equation becomes $\left(y - 3\right) + 3 y = 13$. Solve this for $y$ to get $y = 4$.

Then, go back to the first equation that says $x = y - 3$ and plug in $y = 4$. So $x = 1$.

Check your work by plugging in the values. $1 = 4 - 3$ and $1 + 3 \left(4\right) = 13$, so we are right.