Question

patterns many native american rugs and blankets incorporate parallelograms into the designs. find the values of x and y so that the quadrilateral shown is a parallelogram. \\(6x + 1\\) \\(2y + 3\\) \\(4y - 7\\) \\(8x - 3\\) \\(x = \\) \\(y = \\)

Explanation:

Step1: Solve for \( x \)

In a parallelogram, opposite sides are equal. So, set \( 6x + 1 = 8x - 3 \).
Subtract \( 6x \) from both sides: \( 1 = 2x - 3 \).
Add 3 to both sides: \( 4 = 2x \).
Divide by 2: \( x = 2 \).

Step2: Solve for \( y \)

Opposite sides are equal, so set \( 2y + 3 = 4y - 7 \).
Subtract \( 2y \) from both sides: \( 3 = 2y - 7 \).
Add 7 to both sides: \( 10 = 2y \).
Divide by 2: \( y = 5 \).

Answer:

\( x = 2 \)
\( y = 5 \)