To solve the given system of equations, we have to multiply the first equation by -1.
[tex]\mleft\{\begin{aligned}-2x+y=2 \\ 2x+4y=8\end{aligned}\mright.[/tex]Then, we sum them.
[tex]\begin{gathered} -2x+2x+y+4y=2+8 \\ 5y=10 \\ y=\frac{10}{5} \\ y=2 \end{gathered}[/tex]Then, we use this value to find x.
[tex]\begin{gathered} 2x-y=-2 \\ 2x-2=-2 \\ 2x=-2+2 \\ 2x=0 \\ x=0 \end{gathered}[/tex]