[tex]\begin{cases}8x+5y=-13\\3x+4y=10\end{cases}[/tex]
Multiply both equations by appropriate constants to get the coefficients of either [tex]x[/tex] or [tex]y[/tex] in both equations to be the same. One choice would be to multiply the first equation by 3 and the second by 8:
[tex]\begin{cases}24x+15y=-39\\24x+32y=80\end{cases}[/tex]
Then subtract either equation from the other to eliminate [tex]x[/tex]. I'll take the first from the second:
[tex](24x+32y)-(24x+15y)=80-(-39)\implies17y=119\implies y=7[/tex]
Then solve for [tex]x[/tex] in either equation. From the second one, we find
[tex]3x+4(7)=10\implies3x=10-28=-18\implies x=-6[/tex]
So the solution to this system is the coordinate pair (-6, 7).
