Answer
The solution is $(-3, 5)$.
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 $y$ term:
$x + 2y = 7$
$-x + 3y = 18$
_____________
$2y = 7$
$3y = 18$
Now we add both sides of the two equations to get:
$5y = 25$
Divide each side by $5$ to solve for $y$:
$y = 5$
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:
$x + 2(5) = 7$
Multiply:
$x + 10 = 7$
Subtract $10$ from each side of the equation to isolate the variable on one side and constants on the other:
$x = -3$
The solution is $(-3, 5)$.
