1. 3.5 Solving systems of equations in 3 variables

2. Select any 2 of the 3 equations and try to eliminate one variable to get an equation with 2 variables
Select a different pair of equations and try to eliminate the same variable as step 1
Combine the equations found from step 1 and step 2 then solve for systems of 2 variable
Substitute the solutions from step 3 to any of the original equations to solve for the last variable

3. 2x – y + z = 10 -6x + 3y – 3z = -30 4x + 2y – 3z = 10 x – 3y + 2z = 8
Step 1: Select equation 1 and 2, then multiply the first equation by 2
(2) 2x – y + z = 10
4x – 2y + 2z = 20
4x + 2y – 3z = 10
8x – z = 30
Step 2: Select eq.1 and 3
(-3) 2x – y + z = 10
-6x + 3y – 3z = -30
x - 3y + 2z = 8
-5x z = -22
Step 3: combine
8x – z = 30
-5x – z = -22
should get x = 4, z = 2
Step 4: Substitute to
2x – y + z = 10
8 - y + 2 = 10
10 – y = 10
y = 0
Solution:
(4, 0, 2)

4. Try:
2x + y - 3z = -4
4x - 2y + z = 9
3x + 5y - 2z = 5
Answer: (2,1,3)

5. Try:
x + y + z = 57
-2x + y = 3
x - z = 6
Answer: (15, 33, 9)