Question

find the values of the variables. then find the side lengths of the square.

Explanation:

Step1: Set equal sides for $y$

All sides of a square are equal, so set two expressions for $y$ equal:
$y-1 = 2y-6$

Step2: Solve for $y$

Rearrange to isolate $y$:
$2y - y = 6 - 1$
$y=5$

Step3: Calculate side length

Substitute $y=5$ into $y-1$:
$5-1=4$

Step4: Set side equal to $x$ expression

Set the side length equal to $4x-20$:
$4x-20=4$

Step5: Solve for $x$

Rearrange to isolate $x$:
$4x=4+20$
$4x=24$
$x=\frac{24}{4}=6$

Answer:

$x=6$, $y=5$
Side length of the square is $4$