Answer
$x = 12$
$y = 4$
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:
$2x - 5 = x + 7$
Add $5$ to each side of the equation to isolate constants on one side of the equation:
$2x = x + 12$
Subtract $x$ from each side of the equation to solve for $x$:
$x = 12$
Let's set the two segments of the other bisected diagonal equal to one another
$6y + 1 = 4y + 9$
Subtract $1$ from each side of the equation to isolate constants on one side of the equation:
$6y = 4y + 8$
Subtract $4y$ from each side of the equation to isolate the variable on the left side of the equation:
$2y = 8$
Divide each side of the equation by $2$ to solve for $y$:
$y = 4$
