Answer
No solution (inconsistent system)
Work Step by Step
Rewrite the first equation in its slope intercept form and compare it to the second.
$$\begin{aligned}
10x-4y&= 30\\
-4y&= -10x+30\\
y&= \frac{10}{4}x-\frac{30}{4}\\
y&= \frac{5}{2} x+\frac{15}{2}.
\end{aligned}$$ Rewrite the system: $$\begin{cases}
y&= \frac{5}{2} x+\frac{15}{2}\\
y & = \frac{5}{2} x+14.
\end{cases}$$ We are asked to use the method of substitution to solve the given system. However, we see that both equations have the same slope but different $y$-intercepts. This means that the lines are parallel. Since parallel lines do not intercept, the system is inconsistent and has no solution.
