\(\left\{{}\begin{matrix}2P+Q=x^2y+6xy^2+3x^2y^2\\P-Q=2x^2-xy^2+3x^2y^2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2P+Q+P-Q=x^2y+6xy^2+3x^2y^2+2x^2-xy^2+3x^2y^2\\Q=P-\left(2x^2-xy^2+3x^2y^2\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3P=x^2y+5xy^2+6x^2y^2+2x^2\\Q=P-\left(2x^2-xy^2+3x^2y^2\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}P=\dfrac{1}{3}x^2y+\dfrac{5}{3}xy^2+2x^2y^2+\dfrac{2}{3}x^2\\Q=\dfrac{1}{3}x^2y+\dfrac{5}{3}xy^2+2x^2y^2+\dfrac{2}{3}x^2-2x^2+xy^2-3x^2y^2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}P=\dfrac{1}{3}x^2y+\dfrac{5}{3}xy^2+2x^2y^2+\dfrac{2}{3}x^2\\Q=\dfrac{1}{3}x^2y+\dfrac{8}{3}xy^2-x^2y^2-\dfrac{4}{3}x^2\end{matrix}\right.\)
