Write a system of two equations in two variables to solve the problem. when fully extended, a ladder is 28 feet in length. if the extension is 4 feet shorter than the base, how long is each part of the ladder? base

Let the base of the ladder be x ft and the extension be y ft.

"when fully extended, a ladder is 28 feet in length."

means: x+y=28

" the extension is 4 feet shorter than the base "

means: y=x-4, that is x-y = 4, (taking y to the side of x, and - 4 to the other side of x and y)

thus, we have the system of equations:

1) x+y = 28

2) x-y=4

adding the 2 equations, we have:

(x+y) + (x-y) = 28+4

2x=32

x=32/2=16

x+y=28, so 16+y=28, thus y=12

Answer: Base: 16, Extension 12