Answer
$(z,q)= (12,-4.5)$ (consistent independent system)
Work Step by Step
Given $$\begin{cases}
q-2.5z&= 23.25\\
6q+5z&= 49.5\\
\end{cases}$$ Rewrite the first equation in its slope intercept form and substitute the result into the second and solve.
$$\begin{aligned}
q-2.5z&= 23.25\\
q&= 2.5z+23.25
\end{aligned}$$ and $$\begin{aligned}
6(2.5z+23.25)+5z&= 49.5\\
15z+5z+139.5&= 49.5\\
20z&= 49.5-139.5\\
z&= -\frac{90}{20}\\
&= -4.5
\end{aligned}$$
Now solve for $q$ using any of the above equations.
$$\begin{aligned}
q &= 2.5(-4.5)+23.25\\
&= 12.
\end{aligned}$$ The solution set is $(z,q)= (12,-4.5)$ . The system is consistent and independent because it has a single solution.
