Can somebody walk me through this please!

x = 5, y = -6, z = -2

Step-by-step explanation:

Given the following systems of linear equations:

Equation 1:   x =  y + 11

Equation 2:  x + 2y - 4z = 1

Equation 3:  2x = 10

In order to use the substitution method, choose one of the given equation where the variable has a coefficient of 1.  We could use Equation 1 and substitute its value into Equation 3:

Use Equation 1: x =  y + 11  substitute into Equation 3 to solve for y:

2x = 10

2(y + 11) = 10

Distribute 2 into the parenthesis:

2y + 22 = 10

2y + 22 - 22 = 10 - 22

2y = -12

y = -6

Substitute the value of y = -6 into Equation 1:

x =  y + 11

x = -6 + 11

x = 5

Substitute the values of x = 5 and y = -6 into Equation 2 to solve for z:

x + 2y - 4z = 1

5 + 2(-6) - 4z = 1

5 - 12 - 4z = 1

-7 - 4z = 1

Add 7 to both sides:

-7 + 7 - 4z = 1 + 7

-4z = 8

Divide both sides by -4 to solve for z:

z = -2

Verify whether the values for x, y, and z satisfy the three equations in the given linear system:

x = 5, y = -6, z = -2

Equation 1:   x =  y + 11

5 = -6 + 11

5 = 5 (True statement)

Equation 2:  x + 2y - 4z = 1

5 + 2(-6) - 4(-2) = 1

5 - 12 + 8 = 1

13 - 12 = 1

1 = 1 (True statement)

Equation 3:  2x = 10

2(5) = 10

10 = 10 (True statement).

Therefore,  x = 5, y = -6, z = -2 satisfy all the equations within the given system.