Given the system of equations :
[tex]\begin{gathered} 2x+5y=-49 \\ -2x+8y=-68 \end{gathered}[/tex]Add the equations to eliminate x :
[tex]\begin{gathered} (2x+5y)+(-2x+8y)=-49+(-68) \\ 2x+5y-2x+8y=-117 \\ (2x-2x)+(5y+8y)=-117 \\ 13y=-117 \end{gathered}[/tex]divide both sides by 13 to find the value of y :
[tex]\begin{gathered} \frac{13y}{13}=\frac{-117}{13} \\ \\ y=-9 \end{gathered}[/tex]To find x , substitute with the value of y at the first equation :
[tex]\begin{gathered} 2x+5\cdot-9=-49 \\ 2x-45=-49 \\ 2x=-49+45 \\ 2x=-4 \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=-2 \\ y=-9 \end{gathered}[/tex]The solution can be written as the order pair (x,y):
[tex](x,y)=(-2,-9)[/tex]