Question

Solve each System:
-2x+4y+4z=24
2z=8
4x+y=11

Answer 1

-2x+4y+4z=24

Move all terms not containing y to the right-hand side of the equation.
4y=2x-4z+24

Divide each term in the equation by 4.
(4y)/(4)=(2x)/(4)-(4z)/(4)+(24)/(4)

Simplify the left-hand side of the equation by canceling the common factors.
y=(2x)/(4)-(4z)/(4)+(24)/(4)

Simplify the right-hand side of the equation by simplifying each term.
y=(x-2z+12)/(2)

Answer 2

2z=8

Divide each term in the equation by 2.
(2z)/(2)=(8)/(2)

Simplify the left-hand side of the equation by canceling the common factors.
z=(8)/(2)

Simplify the right-hand side of the equation by simplifying each term.
z=4

Answer 3

4x+y=11

Since 4x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4x from both sides.
y=-4x+11

Answer 4

4x+y=11

Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
4x=-y+11

Divide each term in the equation by 4.
(4x)/(4)=-(y)/(4)+(11)/(4)

Simplify the left-hand side of the equation by canceling the common factors.
x=-(y)/(4)+(11)/(4)

Combine the numerators of all expressions that have common denominators.
x=(-y+11)/(4)