# Chapter 6 - Polygons and Quadrilaterals - Chapter Review - Page 421: 16

$x = 2$ $y = 5$

#### 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 $y$: $y = 5$

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