Answer
The solution to this system of equations is $(-2, 3)$.
Work Step by Step
Rewrite the equations so that the variables are on one side while the constant is on the other:
$-2x - 5y = -11$
$ 9x + 5y = -3$
We see that in the two equations, the $y$ term is exactly the same except they have opposite signs. If we add these two equations together, we can eliminate the variable $y$ and just deal with one variable instead of two:
$(-2x-5y)+(9x+5y)=-11+(-3)\\
7x = -14$
Divide each side by $7$ to solve for $x$:
$x = -2$
Now that we have the value for $x$, we can plug it into one of the equations to solve for $y$. Let's plug in the value for $x$ into the first equation:
$11 - 5y = 2(-2)$
$11 - 5y = -4$
Now, we subtract $11$ from both sides of the equation to isolate constants to the right side of the equation:
$-5y = -15$
Divide both sides by $-5$ to solve for $y$:
$y = 3$
The solution to this system of equations is $(-2, 3)$.
