Answer
$(h,g)= (7,2)$ (consistent independent system)
Work Step by Step
Given $$\begin{cases}
g+5h&= 37\\
3g+4h&= 34.
\end{cases}$$ Rewrite the first equation in its slope intercept form and substitute the result into the second and solve.
$$\begin{aligned}
g+5h&= 37\\
g&= -5h+37
\end{aligned}$$ and $$\begin{aligned}
3(-5h+37)+4h&= 34\\
-15h+4h+111&= 34\\
-11h&= 34-111\\
h&= \frac{77}{11}\\
&= 7.
\end{aligned}$$ Now solve for $g$ using any of the above equations.
$$\begin{aligned}
g &= -5(7)+37\\
&= 2.
\end{aligned}$$ The solution set is $(h,g)= (7,2)$ . The system is consistent and independent because it has a single solution.
