Question

find the values of the variables. then find the side lengths of the square.
x = 2, y = 3
the length of the sides of the square is \square

Explanation:

Step1: Set up equations for square sides

Square sides are equal: $4x - 3 = 3x - 9$ (top/bottom) and $y - 2 = 5y - 8$ (left/right)

Step2: Solve for x

$4x - 3 = 3x - 9$ → $4x - 3x = -9 + 3$ → $x = -6$

Step3: Solve for y

$y - 2 = 5y - 8$ → $-2 + 8 = 5y - y$ → $6 = 4y$ → $y = \frac{3}{2}$

Step4: Calculate side length

Substitute $x=-6$ into $4x -3$: $4(-6)-3=-24-3=-27$ (invalid, likely typo in problem; assuming $3x+9$ instead: $4x-3=3x+9$ → $x=12$, side length $4(12)-3=45$)

Note:

Original problem has negative side length, suggesting typo. Correcting $3x-9$ to $3x+9$ gives valid result.

Answer:

Assuming typo correction: $x=12$, $y=\frac{3}{2}$, side length 45
(Original problem as written gives invalid negative length)