Answer
$x = 5$
$y = 7$
Work Step by Step
Theorem 6-6 states that in a quadrilateral that is a parallelogram, its diagonals bisect one another.
We can now deduce that for bisector $\overline{PR}$, $\overline{PT}$ is congruent to $\overline{TR}$. For $\overline{QS}$, $\overline{QT}$ is congruent to $\overline{TS}$. Let's set up the two equations reflecting this information:
$PT = TR$
$QT = TS$
Let's substitute in what we know:
$x + 2 = y$
$2x = y + 3$
We can solve for both $x$ and $y$ by setting the two equations up as a system of equations:
$x + 2 = y$
$2x = y + 3$
Let's get all the variables on one side and the constants on the other:
$x - y = -2$
$2x - y = 3$
$x - y = -2$
$-2x + y = -3$
Now, we add the two equations together:
$-x = -5$
Divide each side by $-1$ to solve for $x$:
$x = 5$
Now that we have the value for $x$, we can plug in this value for $x$ into one of the original equations to find $y$:
$5 + 2 = y$
Add to solve for $y$:
$y = 7$
