Write a system of equations to represent the situation and find the dimension of the rectangle

Question

The length y of a rectangle is four less than three times the width x. The perimeter of the rectangle is 16 cm. Write a system of equations to represent this situation and find the dimensions of the rectangle

Answer 1

Equation 1 is the perimeter of the rectangle. Equation 2 is given in the problem. Equation 3 is another equation for the perimeter given in the problem.

1. P=2y+2x
2. y=3x-4
3. P=16

So from here, you substitute equations 2 and 3 into equation 1 and solve for x as follows:

16=2(3x-4)+2x

16 = 6x-8+2x = 8x-8

=> 24 = 8x

=> x=3

Then you plug x=3 into equation 2 to solve for y:

y=3*3-4=9-4=5

So the dimensions are x=3 and y=5