Answer
$x = 3$
$y = 4$
Work Step by Step
Parallelograms have opposite sides that are congruent. In order for $RSTV$ to be a parallelogram, we must have $RV$ and $TS$ equal to one another and $VT$ and $SR$ equal to one another. Let's set $RV$ and $TS$ equal to one another first:
$RV = TS$
Let's plug in what we are given in the diagram:
$2x + 3 = y + 5$
Now, let's set $VT$ and $SR$ equal to one another:
$VT = SR$
Plug in what we are given:
$5x = 4y - 1$
We have two equations and two variables. We can use the elimination method by setting up the system of equations to solve for one variable:
$2x + 3 = y + 5$
$5x = 4y - 1$
Let's get all the variables on one side and the constants on the other:
$2x - y = 2$
$5x - 4y = -1$
We have to modify one of the equations because we need one of the variables in both equations to differ only in sign. Let's multiply the first equation by $-4$:
$-8x + 4y = -8$
$5x - 4y = -1$
Now, we can add the two equations together:
$-3x = -9$
Divide each side by $-3$ to solve for $x$:
$x = 3$
Now that we have the value for $x$, we can plug in this value for $x$ into one of the original equations to find $y$:
$5x = 4y - 1$
Substitute $3$ for $x$:
$5(3) = 4y - 1$
Multiply to simplify:
$15 = 4y - 1$
Add $1$ to both sides of the equation to solve for $y$:
$4y = 16$
Divide each side by $4$ to solve for $y$:
$y = 4$
