Answer
The solution is $(-3, 4)$.
Work Step by Step
The coefficients of the $x$ term differ only in sign, so if we add these equations without modification, we will cancel out the $x$ term and can then solve for $y$:
Let us add the equations. First, we cancel out the $x$ term:
$2x + y = -2$
$-2x - 3y = -6$
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$y = -2$
$-3y = -6$
Now we add both sides of the two equations to get:
$-2y = -8$
Divide each side by $-2$ to solve for $y$:
$y = 4$
Now that we have the value for $y$, we can plug this value into one of the equations to solve for $x$. Let's use the first equation:
$2x + 4 = -2$
Subtract $4$ from each side of the equation to isolate the variable on one side of the equation and constants on the other:
$2x = -6$
Divide each side of the equation by $2$ to solve for $x$:
$x = -3$
The solution is $(-3, 4)$.
