Find the value of x and y. show your work

The lines on the sides represent the two sides are equal.

Hence, the side, AC=PR, the sides with one line each.

The sides, AB=PQ, the sides with two line each.

The sides, BC= QR, the sides with three line each.

Hence, By SSS congurency the two triangles are congurent.

As the two triangles are congurent.

And, The sides are equal

AB=PQ

So, 7x-4=31

Adding 4 on both sides

7x-4+4=31+4

7x=35

To solve for x, Divide by 7 on both sides

x=35/7

x=5

Also, BC=QR

So,4y+8=24

Subtracting 8 from both sides

4y+8-8=24-8

4y+0=16

4y=16

To solve for y, Let us divide by 4 on both sides

4y/4=16/4

y=4