L = length / W = width / P = Perimeter
L=2W-3 (three feet less than twice its width)
To find a perimeter the formula is 2W+2L=P
So if we have two formulas with the same variables (L & W)
We can substitute one for the other. In this case we will take L=2w-3 and input it in for "L" in 2W+2L=P. We know P is 42 so substituting L into the equation will look as such.
2W + 2 ( 2W - 3 ) = 42
2W + 4W - 6 = 42 (Multiply both "2W" & "3" by "2"
6W - 6 = 42 (Add like values)
6W = 48 (Add value to opposite of the equation
W = 8 (Divide each side by 6 to get the value of W)
Now that we have W, we need to take W and substitute it into the first equation, giving us
L = 2 (8) - 3
L = 16 - 3 (PEMDAS)
L = 13 (PEMDAS)
Now that we have both L and W we can plug our answers into the perimeter formula to check our answer.
2 (8) + 2 (13) = 42
16 + 26 = 42 (PEMDAS)
42 = 42 (PEMDAS)
The solution matches meaning the answer is correct.