Answer
$y = 28$
$x = 29$
Work Step by Step
In a parallelogram, opposite angles are congruent, so let us set our opposite angles equal to one another:
$m \angle A = m \angle C$
$m \angle B = m \angle D$
Let's substitute what we know:
$4x = 4y + 4$
$2x + 6 = 3y - 20$
Let's move the variables to the left and constants to the right in both equations:
$4x - 4y = 4$
$2x - 3y = -26$
Let's convert one equation so that one of the variables in both equations is the same but differing in sign:
$4x - 4y = 4$
$-4x + 6y = 52$
Now we can add the two equations together:
$2y = 56$
Divide both sides by $2$ to solve for $y$:
$y = 28$
Now that we have the value for $y$, let us substitute it into one of the equations to solve for $x$:
$4x = 4(28) + 4$
Multiply first, according to order of operations:
$4x = 112 + 4$
Add to simplify:
$4x = 116$
Divide both sides by $4$ to solve for $x$:
$x = 29$
