Answer
The solution is $(3, 1)$.
Work Step by Step
In this case, we first want to modify both equations so that one of the variable terms is the same in both equations but with differing signs. Let's multiply the first equation by $3$ and the second equation by $-2$:
$$6x + 12y = 30\\-6x - 10y = -28$$
We now can add the equations together:
\begin{align*}
6x + 12y = 30\\
\underline{-6x - 10y = -28}\\
2y=2\\
y=\frac{2}{2}\\
y=1
\end{align*}
Substitute this value for $y$ into the first equation to find $x$:
$$2x + 4(1) = 10\\2x + 4 = 10\\2x=10-4\\2x = 6\\x=\frac{6}{2}\\x=3$$
The solution is $(3, 1)$.
