Given the system of equations :
[tex]\begin{gathered} -8x-4y=-4 \\ -5x-4y=2 \end{gathered}[/tex]Subtract the first equation from the second equation :
So,
[tex]\begin{gathered} -5x-4y-(-8x-4y)=2-(-4) \\ \\ -5x-4y+8x+4y=6 \\ 3x=6 \\ \\ x=\frac{6}{3}=2 \end{gathered}[/tex]substitute at the first equation to find y :
So
[tex]\begin{gathered} -8\cdot2-4y=-4 \\ -16-4y=-4 \\ -4y=-4+16 \\ -4y=12 \\ \\ y=\frac{12}{-4}=-3 \end{gathered}[/tex]So, the solution of the system is:
[tex]\begin{gathered} x=2 \\ y=-3 \end{gathered}[/tex]