---------------------------------------------------------------- Define x and y: ---------------------------------------------------------------- Let the length be x. Let the width be y.
---------------------------------------------------------------- Construct equations and solve for x and y: ---------------------------------------------------------------- 2x + 2y = 56 ---------------------- (1) 2(x+8) + 4y = 82 -----------------------(2)
---------------------------------------------------------------- From equation 1: ---------------------------------------------------------------- 2x + 2y = 56 x + y = 28 x = 28 - y
---------------------------------------------------------------- Substitute x = 28 - y into equation 2: ---------------------------------------------------------------- x + 2y = 33 (28 - y) + 2y = 33 28 - y + 2y = 33 y = 5
---------------------------------------------------------------- Substitute y = 5 into equation 1: ---------------------------------------------------------------- x = 28 - y x = 28 - 5 x = 23
---------------------------------------------------------------- Find Length and Width ---------------------------------------------------------------- Length = x = 23 m Width = y = 5m
---------------------------------------------------------------- Answer: Length = 23m and Width = 5m ----------------------------------------------------------------
Commutative means 'you can swap them'. I.e., a+b = b+a, addition is commutative. Subtraction is not.
The first answer: <span>2(6a − 3) = (6a − 3) ⋅ 2 is an example where 2 and (6a-3) are the factors that can be swapped, because multiplication is commutative.</span>
