Answer :
We must solve the following system of equation:
[tex]\begin{gathered} x=y-8 \\ -x-y=0 \end{gathered}[/tex]Solving by elimination method.
If we add the first equation wih the second one, we obtain
[tex]x-x-y=y-8+0[/tex]which is equal to
[tex]-y=y-8[/tex]If we move y to the left hand side, we have
[tex]\begin{gathered} -y-y=-8 \\ \\ \end{gathered}[/tex]and it reads
[tex]\begin{gathered} -2y=-8 \\ y=\frac{-8}{-2} \\ y=4 \end{gathered}[/tex]We obtained the first result y=4. Now, we can substitute this value into one of the two equation. If we substitute y=4 in the first equation, we have
[tex]x=4-8[/tex]which gives x=-4. Finally, the answer is x=-4 and y=4. The coordinate of this solution is (-4,4).