Can somebody please walked through this, I'm so confused and I have a test in 6 hours...

x = 4, y = 4, z = 4

Step-by-step explanation:

Given the following systems of linear equations:

Equation 1:    x = 5z - 16

Equation 2 :  -4x + 4y - 5z = -20

Equation 3:    y = -z + 8

Using the substitution method, we could either use the value for x in Equation 1, or the value of y in Equation 3 to substitute in the other given equations.

Let's use Equation 3, and substitute the value of y = -z + 8 into Equation 2:

Equation 3:    y = -z + 8

Equation 2 :  -4x + 4y - 5z = -20

-4x + 4(-z + 8) - 5z = -20

-4x - 4z + 32 - 5z = -20

-4x - 9z + 32 = -20

Using Equation 1, substitute the value of x = 5z - 16 into the previous step:

Equation 1:    x = 5z - 16 into:

-4(5z - 16) - 9z + 32 = -20

-20z + 64 - 9z + 32 = -20

-29z + 96 = -20

Subtract 96 from both sides:

-29z + 96 - 96 = -20 - 96

-29z = -116

Divide both sides by -29:

z = 4

Substitute the value of z = 4 into Equation 3:

Equation 3:    y = -z + 8

y = -(4) + 8

y = 4

Substitute the values of z into Equation 1 to solve for x:

Equation 1:    x = 5z - 16

x = 5(4) - 16

x = 20 - 16

x = 4

Therefore, x = 4, y = 4, and z = 4.

Substitute the values for x, y, and z into the given system to verify that their values are the solutions.

x = 4, y = 4, z = 4

Equation 1:    x = 5z - 16

4 = 5(4) - 16

4 = 20 - 16

4 = 4 (True statement).

Equation 2 :  -4x + 4y - 5z = -20

-4(4) + 4(4) - 5(4) = -20

-16 + 16 - 20 = - 20

0 - 20 = -20

-20 = -20 (True statement).

Equation 3:    y = -z + 8

y = -z + 8

4 = -(4) + 8

4 = -4 + 8

4 = 4 (True statement).

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.

so, converting firstly the mixed fractions to improper fractions and then "adding".