3.5 Solving systems of equations in 3 variables

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

3

• 2x y z 10
• 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 3z 10
• 4x 2y 2z 20
• 4x 2y 3z 10
• 8x z 30
• Step 2 Select eq.1 and 3
• (-3) 2x y z 10
• x 3y 2z 8

• -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)