[tex]\large\boxed{\begin{array}{l}\sf A=\begin{pmatrix}\sf2&\sf1\\\sf x&\sf2\end{pmatrix},B=\begin{pmatrix}\sf1&\sf y\\\sf1&\sf2\end{pmatrix},A\times B=\begin{pmatrix}\sf3&\sf0\\\sf5&\sf z\end{pmatrix}\end{array}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\sf A\times B=\begin{pmatrix}\sf2+1&\sf0+z\\\sf x+2&\sf xy+4\end{pmatrix}=\begin{pmatrix}\sf3&\sf0\\\sf5&\sf z\end{pmatrix}\\\\\sf\begin{pmatrix}\sf3&\sf z\\\sf x+2&\sf xy+4\end{pmatrix}=\begin{pmatrix}\sf3&\sf0\\\sf5&\sf z\end{pmatrix}\\\\\begin{cases}\sf z=0\\\sf x+2=5\\\sf xy+4=z\end{cases}\\\\\sf z=0\\\sf x+2=5\\\sf x=5-2\\\sf x=3\\\sf xy+4=z\\\sf 3\cdot y+4=0\\\sf 3y=-4\\\sf y=-\dfrac{4}{3}\end{array}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\sf x+y+z=3+\bigg(-\dfrac{4}{3}\bigg)+0=3-\dfrac{4}{3}\\\\\sf x+y+z=\dfrac{9-4}{3}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x+y+z=\dfrac{5}{3}}}}}\end{array}}[/tex]