Answer
$x = 2$
$y = 5$
Work Step by Step
In parallelogram $ABCD$, $AB$ is congruent to its opposite side $CD$, and $BC$ is congruent to $DA$. Let us set opposite sides equal to one another:
$AB = CD$
$BC = DA$
Let's plug in the expressions given for each side:
$2y + 1 = 7x - 3$
$y + 1 = 3x$
Let's move all variables to the left side of the equation and all constants to the right side of the equation:
$-7x + 2y = -4$
$-3x + y = -1$
Now we have a system of equations. Let's convert one of the equations so that one of the variables is the same in both equations but differing in sign:
$-7x + 2y = -4$
$6x - 2y = 2$
We can now add the equations together:
$-x = -2$
Divide each side by $-1$ to solve for $x$:
$x = 2$
We can now substitute $2$ for $x$:
$-3(2) + y = -1$
Multiply first:
$-6 + y = -1$
Add $6$ to each side of the equation to solve for $y$:
$y = 5$
