Answer
$x = \frac{5}{3}$
$y = \frac{9}{2}$
Work Step by Step
This quadrilateral is a kite because consecutive sides are congruent. We can find the values for each of the sides by setting consecutive sides equal to one another. Let's start with the two consecutive sides whose expressions have an $x$ term in them:
$6x + 1 = 3x + 6$
Subtract $1$ from each side of the equation to move constants to the right side of the equation:
$6x = 3x + 5$
Subtract $3x$ from each side of the equation to move variables to the left side of the equation:
$3x = 5$
Divide both sides by $3$ to solve for $x$:
$x = \frac{5}{3}$
Let's set the other two consecutive sides equal to one another to find the value for $y$:
$2y + 6 = 4y - 3$
Subtract $6$ from each side of the equation to move constants to the right side of the equation:
$2y = 4y - 9$
Subtract $4y$ from each side of the equation to move variables to the left side of the equation:
$-2y = -9$
Divide both sides by $-2$ to solve for $y$:
$y = \frac{9}{2}$
