I guess by "combination" you mean elimination. You multiplied the second equation by -2, so the system is
[tex]\begin{cases}2x+5y=-1\\-2x-4y=0\end{cases}[/tex]
Then eliminating [tex]x[/tex] by adding the first equation to the second, you'd end up with
[tex](2x+5y)+(-2x-4y)=-1+0\implies(2x-2x)+(5y-4y)=-1\implies y=-1[/tex]
so you all you did was forget about the -1 from the first equation.
From here, you have
[tex]x+2y=0\implies x=-2y[/tex]
so if [tex]y=-1[/tex], then [tex]x=-2(-1)=2[/tex]. So the solution would be (2, -1).
