Answer
The solution to this system of equations is $w = -2$ and $y = -4$.
Work Step by Step
We see that in the two equations, the $y$ term is the 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:
$(2w+5y)+(3w-5y)=-24+14\\
5w=-10$
Divide each side by $5$ to solve for $w$:
$w = -2$
Now that we have the value for $w$, we can plug it into one of the equations to solve for $y$.
Let us plug the value for $w$ into the second equation:
$3(-2) - 5y = 14$
$-6 - 5y = 14$
Now, we add $6$ to both sides of the equation to isolate constants to the right side of the equation:
$-5y = 20$
Divide both sides by $-5$ to solve for $y$:
$y = -4$
The solution to this system of equations is $w = -2$ and $y = -4$.
