I'm having difficulties in solving the simultaneous equations
$$
\begin{cases}
\sin(x+y)=\frac{1}{\sqrt{2}}\\
\cos(2x+y)=\frac12
\end{cases}
$$
for $0^{\circ}\le x,y\le 90^{\circ}$.

The answer is $x=15^{\circ}$ degrees and $y= 30^{\circ}$.