Question

For each rectangle below, write a linear equation that represents the area y of the rectangle. Solve this system of two linear equations by graphing. Interpret your solution.

Answer 1

(5,24)

• The two areas are the same.

• To find the area, we multiply the side lengths. Y=area

Rectangle 1: side lengths 4 and (x+1)

y=4(x+1)= 4x+4

Rectangle 2: side lengths 3 and (2x-2)

y=3(2x-2)= 6x-6

• Since the two areas are same, we can conclude that

4x+4=6x-6

• Now, simplify.

-2x=-10, x=5

• Since x is 5, we can plug it into the equations to find y.

Option 1 with rectangle 1: y=4(5)+4, y=24

Option 2 with rectangle 2: y=6(5)-5, y=24

I graphed the linear equation on desmos.