Answer
$\left\{ \left( -4,4 \right) \right\}$ Is the solution of the system of equations.
Work Step by Step
Step 1: And solve for y in the second equation to obtain the value of y in terms of x:
Since, $y=\frac{3}{4}x+7$
Step 2:
Put $y=\frac{3}{4}x+7$ in the first equation to obtain the value of x:
$\begin{align}
& \frac{3}{4}x+7=-\frac{1}{2}x+2 \\
& \frac{3}{4}x+\frac{1}{2}x=2-7 \\
& \frac{5}{4}x=-5 \\
& x=-4
\end{align}$
Step 3: Now, put the value, $x=-4$ in the second equation to obtain the value of y:
$\begin{align}
& y=\frac{3}{4}\left( -4 \right)+7 \\
& =-3+7 \\
& =4
\end{align}$
Thus, the solution set $\left( x,y \right)$ to the system of equation is $\left\{ \left( -4,4 \right) \right\}$.
