## Intermediate Algebra: Connecting Concepts through Application

$(3, 2)$
Add the equations together: \begin{array}\\ x+4y=11\\ \underline{5x-4y=7}\\ 6x+0y=18\\\\ \end{array} Solve for $x$ to obtain: \begin{align*} 6x&=18\\ x&=\frac{18}{6}\\ x&=3\end{align*} Substitute $3$ to $x$ in the first equation to obtain: \begin{align*} x+4y&=11\\ 3+4y&=11\\ 4y&=11-3\\ 4y&=8\\ y&=\frac{8}{4}\\ y&=2 \end{align*} Check by substituting $3$ to $x$ and $2$ to $y$ in the second equation to obtain: \begin{align*} 5(3)-4(2)&=7\\ 15-8&=7\\ 7&\stackrel{\checkmark}=7 \end{align*} Therefore, the solution is $(3, 2)$.