Answer
$x = 2$
$y = 6$
Work Step by Step
Theorem 6-6 states that in a quadrilateral that is a parallelogram, its diagonals bisect one another. This means that each segment of the bisected diagonal is equal.
We can set the two segments of the bisected diagonals equal to one another:
$2x = 4$
Divide by $2$ on each side of the equation to solve for $x$:
$x = 2$
Let's set the two segments of the other bisected diagonal equal to one another
$y - 1 = 2y - 7$
Add $1$ to each side of the equation to isolate constants on one side of the equation:
$y = 2y - 6$
Subtract $2y$ from each side of the equation to isolate the variable on the left side of the equation:
$-y = -6$
Divide each side of the equation by $-1$ to solve for $y$:
$y = 6$
