Since we are trying to find the values of two variables (the length L and the width W), we need at least two equations. The perimeter of the rectangle is 42 inches, and the length is 5 inches longer than the width. Mathematically, we get our two equations from these two statements.
First, since the perimeter is 42 inches, we add the four sides and get L + L + W + W = 42. Adding like terms gives us
2L + 2W = 42
Next, the length is 5 inches longer than the width, so
L - 5 = W
We then solve these two equations for L and W. I will use substitution, but elimination would also work.
2L + 2W = 42
L - 5 = W
2L + 2(L-5) = 42
2L + 2L - 10 = 42
4L - 10 = 42
4L = 52
L = 13
Having solved for L, we can now substitute 13 for L in L - 5 = W to solve for W.
13 - 5 = W
W = 8
Our final step is to check by plugging our values into the original equations and making sure they work:
2(13) + 2(8) = 42 (Correct)
13 - 5 = 8 (Correct)