Question

Solve the system by elimination. SHOW WORK

-2X + 2Y + 3Z=0
-2X - Y + Z=-3
2X +3Y +3Z=5

Answer 1

The answer is 1. -2x + 2y + 3z = 0

Steps

First, subtract + 2y + 3z from both sides

-2x + 2y + 3z - (2y + 3z) = 0 - (2y + 3z)

Simplify

-2x = -3z - 2y

Then, divide both sides by -2

-2x/-2 = -3z/-2 - 2y/-2

Then, simplify

x = - -3z - 2y/2

2. -2x - y + z = -3

Steps

First, subtract -y + z from both sides

-2x - y + z - (-y + z) = -3 - (-y + z)

Simplify,

-2x = -3 + y - z

Then, divide both sides by -2

-2x/ -2 = - 3/-2 + y/-2 - z/-2

Simplify,

x = - -3 + y - z/2

3. 2x + 3y + 3z = 5

Steps

First, subtract + 3y + 3z from both sides

2x + 3y + 3z - (3y + 3z) = 5 - (3y + 3z)

Simplify,

2x = 5 - 3y - 3z

Then, divide both sides by 2

2x/2 = 5/2 - 3y/2 - 3z/2

Then, simplify

x = 5 - 3y - 3z/2

Answer 2

1. -2x + 2y + 3z = 0
Steps
First, subtract + 2y + 3z from both sides
-2x + 2y + 3z - (2y + 3z) = 0 - (2y + 3z)
Simplify
-2x = -3z - 2y
Then, divide both sides by -2
-2x/-2 = -3z/-2 - 2y/-2
Then, simplify
x = - -3z - 2y/2

2. -2x - y + z = -3
Steps
First, subtract -y + z from both sides
-2x - y + z - (-y + z) = -3 - (-y + z)
Simplify,
-2x = -3 + y - z
Then, divide both sides by -2
-2x/ -2 = - 3/-2 + y/-2 - z/-2
Simplify,
x = - -3 + y - z/2

3. 2x + 3y + 3z = 5
Steps
First, subtract + 3y + 3z from both sides
2x + 3y + 3z - (3y + 3z) = 5 - (3y + 3z)
Simplify,
2x = 5 - 3y - 3z
Then, divide both sides by 2
2x/2 = 5/2 - 3y/2 - 3z/2
Then, simplify
x = 5 - 3y - 3z/2