Question

(Picture included) Where did I go wrong here? (Using the combination method)

Answer 1

I guess by "combination" you mean elimination. You multiplied the second equation by -2, so the system is

$\begin{cases}2x+5y=-1\\-2x-4y=0\end{cases}$

Then eliminating $x$ by adding the first equation to the second, you'd end up with

$(2x+5y)+(-2x-4y)=-1+0\implies(2x-2x)+(5y-4y)=-1\implies y=-1$

so you all you did was forget about the -1 from the first equation.

From here, you have

$x+2y=0\implies x=-2y$

so if $y=-1$, then $x=-2(-1)=2$. So the solution would be (2, -1).