Answer
$y = 4$
$x = 5$
Each side of the square has a length of $3$.
Work Step by Step
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 $3$.
