Answer
The solution set is $\left\{(5, 0)\right\}$.
Work Step by Step
By adding $7y$ to both sides of the equation, first equation is equivalent to
\begin{align*}
3x-7y+7y&=15+7y\\
3x&=15+7y\end{align*}
Since $3x=15+7y$, substitute $15+7y$ to $3x$ in the second equation to obtain:
\begin{align*}
3x+7y&=15\\
15+7y+7y&=15\\
15+14y&=15\\
14y&=0\\
y&=0
\end{align*}
Plug $y=0$ into $3x-7y=15$, the solve for $x$ o obtain:
\begin{align*}3x-7y&=15\\
3x-7(0)&=15\\
3x&=15\\
x&=\frac{15}{3}\\
x&=5\end{align*}