Answer:
length= 35 feet and width= 10 feet
Step-by-step explanation:
You are given the perimeter of the rectangular deck is
90 feet.
2 x length + 2 x width = 90 You are also given that the deck's length is 5 feet less than 4 times it's width. That is length = 4 x width - 5
Those two equations are your system of linear equations. The second equation can be plugged into the first equation. This gives us an equation entirely in terms of width.
2x (4 x width - 5) + 2 x width =90
Distribute the 2 though
8 x width - 10 + 2 x width = 90
Combine like terms with width.
10 x width - 10 = 90
Add 10 to both sides.
10 x width = 100
Divide both sides by 10 width = 100
Now you can plug width into your original equation for length above. Recall: length = 4 x width - 5
Length = 4 x 10 - 5
Length = 40 - 5
Length = 35
