Given the equations:
[tex]\begin{gathered} -5x+9y=-37 \\ -x+2y=-9 \end{gathered}[/tex]Solve for x in the second equation:
[tex]\begin{gathered} -x+2y-2y=-9-2y \\ -x=-9-2y \end{gathered}[/tex]Multiply by (-1) on both sides:
[tex]\begin{gathered} \lparen-1)(-x)=(-1)(-9-2y) \\ x=9+2y \end{gathered}[/tex]Substitute x in the first equation:
[tex]-5(9+2y)+9y=-37[/tex]Simplify:
[tex]\begin{gathered} -45-10y+9y=-37 \\ -45-y=-37 \end{gathered}[/tex]Solve for y:
[tex]\begin{gathered} -45-y+45=-37+45 \\ -y=8 \\ \frac{-y}{-1}=\frac{8}{-1} \\ y=-8 \end{gathered}[/tex]Then, substitute y = -8 and solve for x:
[tex]x=9+2(-8)=9-16=-7[/tex]Answer:
x = -7
y = -8
