Answer
$x = 5$
$y = 8$
Work Step by Step
We are given a parallelogram, so we know that the diagonals of a parallelogram bisect one another. Therefore, the segments of a bisected diagonal are equal to one another.
$\overline{RT}$ is bisected by $\overline{SV}$, so we can set the two segments of $\overline{RT}$ equal to one another. Conversely, $\overline{VS}$ is bisected by $\overline{VP}$, so we can set the two segments of $\overline{PS}$ equal to one another:
$\overline{RP} = \overline{PT}$
$\overline{VP} = \overline{PS}$
Let's plug in the expressions we are given into the two equations:
$2x = y + 2$
$y = x + 3$
We can solve for both $x$ and $y$ by setting the two equations up as a system of equations:
$2x = y + 2$
$y = x + 3$
Let's get all the variables on one side and the constants on the other:
$2x - y = 2$
$-x + y = 3$
We don't have to modify any of the equations because one of the variables in each of the equations differs only in sign.
Now, we can add the two equations together:
$x = 5$
Now that we have the value for $x$, we can plug in this value for $x$ into one of the original equations to find $y$:
$y = x + 3$
Substitute $5$ for $x$:
$y = 5 + 3$
Add to solve for $y$:
$y = 8$
