Question

Use a matrix to find the solution to the system of equations.

{-8x-8y=-16
{6x-9y=-108


(–6, 8)
(–6, 8)

(6, 8)
(6, 8)

(8, –6)
(8, –6)

(6, –8)
(6, –8)

Answer 1

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

The length of a rectangle is 8.75 cm more than 3 times the width. If the perimeter of the rectangle is 89.5 cm, what are its dimensions?

Answer 2

(6, 8)
(6, 8) is the solution to the system of equations.

Answer 3

Let's assume the width of the rectangle is x cm.

According to the given information, the length of the rectangle is 8.75 cm more than 3 times the width.
So, the length of the rectangle would be (3x + 8.75) cm.

The formula for the perimeter of a rectangle is given by:
Perimeter = 2(length + width)

Substituting the length and width values into the equation, we get:
89.5 = 2((3x + 8.75) + x)

Simplifying the equation:
89.5 = 2(4x + 8.75)
89.5 = 8x + 17.5

Rearranging the equation:
8x = 89.5 - 17.5
8x = 72

Dividing both sides by 8:
x = 9

So, the width of the rectangle is 9 cm.

Substituting this value back into the length equation:
Length = 3x + 8.75
Length = 3 * 9 + 8.75
Length = 27 + 8.75
Length = 35.75

Therefore, the dimensions of the rectangle are:
Width = 9 cm
Length = 35.75 cm