Question

The perimeter of a picture frame is 68 inches. The difference between the length of the frame and three times its width is 2. The system of equations

Answer 1

The width of the frame is 8 inches and the length of the frame is 26 inches

Explanation:

The complete question in the attached figure

Let

L ----> the length of the frame in inches

W ---> the width of the frame in inches

we have

`2L+2W=68` ----> equation A

`2L-6W=4` ----> equation B

Solve the system by elimination

Subtract equation B from equation A

`2L+2W=68\\-(2L-6W)=-4\\---------\\2W+6W=68-4\\8W=64\\W=8\ in`

Find the value of L

substitute the value of W in any equation

`2L+2(8)=68`

`2L+16=68`

`2L=68-16`

`2L=52`

`L=26\ in`

therefore

The width of the frame is 8 inches and the length of the frame is 26 inches