Answer
No solution
Work Step by Step
Given $$\begin{cases}
3 x+6 y=20 \\
4 y=-2 x+15.
\end{cases}$$ Write $y$ as a function of $x$ in each of the two lines.
\begin{equation}
\begin{aligned}
3 x+6 y&=20\\
y&=\frac{20}{6}-\frac{3x}{6}\\
\implies y&= -\frac{1}{2}x+ \frac{10}{3}\\
4 y&=-2 x+15\\
\implies y&= -\frac{1}{2}x+\frac{15}{4}.
\end{aligned}
\end{equation} At this point, we see that the lines are parallel and independent. This means that there is no common point to the lines. Hence, there is no solution for the system.
. See the graph of the functions for further proof.
