First, we multiply the first equation by 2.
[tex]\begin{gathered} (2)(-5x-y)=(2)\cdot4 \\ -10x-2y=8 \end{gathered}[/tex]
Then, we sum this equation with the second one in the given system.
[tex]\begin{gathered} \mleft\{\begin{aligned}-10x-2y=8 \\ 10x+2y=8\end{aligned}\mright. \\ 10x-10x+2y-2y=8+8 \\ 0x+0y=16 \\ 0=16 \end{gathered}[/tex]
As you can observe, we've got a false result because zero is not equal to 16.
Therefore, the system has no solutions at all.
