1. The length of a rectangle is twice its width. The perimeter of the rectangle is 24 inches. Write a system of equations in 2 variables. Use substitution to solve the problem.

A. Equation 1: L = 2W
L= 2(4) = 8

Equation 2: 2L + 2W = 24
2(2W) + 2W = 24
6W = 24
W = 24/6 = 4

(i would like help checking the Equations)

The answer is 16

Let's go through the equations and check them together.

Equation 1: L = 2W
In this equation, L represents the length of the rectangle, and W represents its width. Since it is given that "The length of a rectangle is twice its width," the equation L = 2W is correct.

Now, let's solve Equation 1 using the given value.
L = 2(4)
L = 8

So, the length of the rectangle is indeed 8.

Now, let's move on to Equation 2: 2L + 2W = 24

In this equation, 2L represents the sum of the two lengths of the rectangle (since there are two lengths in a rectangle) and 2W represents the sum of the two widths (again, two widths in a rectangle). It is given that "The perimeter of the rectangle is 24 inches," so the equation 2L + 2W = 24 is correct.

Now let's solve Equation 2:
2(8) + 2W = 24
16 + 2W = 24
2W = 24 - 16
2W = 8
W = 8 / 2
W = 4

So, the width of the rectangle is indeed 4.

Both equations are correctly set up, and when solved, they give the values of length (L = 8) and width (W = 4), which satisfy the given conditions.

To check if the equations are correct, let's substitute the value of W = 4 into Equation 1 and Equation 2:

Equation 1: L = 2W
L = 2 * 4
L = 8

Equation 2: 2L + 2W = 24
2(8) + 2(4) = 24
16 + 8 = 24
24 = 24

Both equations hold true when W = 4 and L = 8. Thus, the equations are correct.

Now let's proceed with solving the system of equations using substitution:

Equation 1: L = 2W

Substitute the value of L from Equation 1 into Equation 2:

2L + 2W = 24
2(2W) + 2W = 24
4W + 2W = 24
6W = 24
W = 24/6
W = 4

Now substitute the value of W = 4 into Equation 1 to find L:

L = 2W
L = 2 * 4
L = 8

Therefore, the width of the rectangle is 4 inches and the length is 8 inches.

ERquation 1.

L = 2 W

2 W = L

Equation 2.

2 W + 2 L = 24

Substitution: 2 W = L

L + 2 L = 24

3 L = 24

L = 24 / 3 = 8 in

L = 2 W

8 = 2 W

8 / 2 = W

W = 4 in