Answer
$x=6, y=10$
Work Step by Step
In a parallelogram, opposite sides are congruent. We can set each set of sides equal to one another to find the values for $x$ and $y$:
Let's tackle one pair of parallel sides first:
$x + 2 = 3x - 10$
Subtract $2$ from each side of the equation to isolate constants to one side:
$x = 3x - 12$
Subtract $3x$ from each side of the equation to isolate the variable to one side of the equation:
$-2x = -12$
Divide both sides by $-2$ to solve for $x$:
$x = 6$
Now let's turn our attention to the other pair of parallel sides:
$6y - 55 = 15 - y$
Add $55$ to each side of the equation to isolate constants to one side:
$6y = 70 - y$
Add $y$ to each side of the equation to isolate the variable to one side of the equation:
$7y = 70$
Divide both sides by $7$ to solve for $y$:
$y = 10$
