To eliminate the y variable we multiply the second equation by -2, then we have:
[tex]\begin{gathered} 5x+2y=-37 \\ -8x-2y=58 \end{gathered}[/tex]now we add the equations:
[tex]\begin{gathered} -3x=21 \\ x=\frac{21}{-3} \\ x=-7 \end{gathered}[/tex]Once we have x we can find y by plugging the value of x into the first equation and solve for y:
[tex]\begin{gathered} 5(-7)+2y=-37 \\ -35+2y=-37 \\ 2y=35-37 \\ y=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]Then the solution is x=-7 and y=-1.
