\(\hept{\begin{cases}x+2y=3\\x^2+xy+2y^2+6y-10=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3-2y\left(1\right)\\\left(3-2y\right)^2+\left(3-2y\right)y+2y^2+6y-10=0\left(2\right)\end{cases}}\)
\(\Leftrightarrow4y^2-3y+1=0\)
\(\Leftrightarrow\orbr{\begin{cases}y=1\\y=-\frac{1}{4}\end{cases}}\)