## Geometry: Common Core (15th Edition)

$y = 4$ $x = 5$ Each side of the square has a length of $3$.
All sides of a square are congruent, so let us take two of the sides and set them equal to one another so we can find the value of one of the variables: $y - 1 = 2y - 5$ $y = 2y - 4$ $-y = -4$ Divide each side of the equation by $-1$ to solve for $y$: $y = 4$ Now, we set the two other opposite sides equal to one another: $2x - 7 = 3y - 9$ Plug in $4$ for $y$: $2x - 7 = 3(4) - 9$ Multiply first, according to order of operations: $2x - 7 = 12 - 9$ $2x = 12 - 9 + 7$ Add or subtract from left to right: $2x = 10$ Divide each side by $2$ to solve for $x$: $x = 5$ If this is a square, then all sides are congruent; therefore, we can solve for one expression to get the lengths of all the sides: side of the square = $y - 1$ Plug in $4$ for $y$: side of the square = $4 - 1$ Subtract to solve: side of the square = $3$ Each side of the square has a length of $3$.