# 3.5 – Solving Systems of Equations in Three Variables.

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3.5 – Solving Systems of Equations in Three Variables

Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2x – y + 3z = - 5

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5]

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 2[2x – y + 3z = - 5] x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 102x – y + 3z = - 5 2[2x – y + 3z = - 5]2x – 3y – 5z = 27 x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 102x – y + 3z = - 5 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 4x – 2y + 6z = -10 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27 x + 2y + z = 10 -3[2x – y + 3z = - 5] 2[2x – y + 3z = - 5] 2x – 3y – 5z = 27 x + 2y + z = 10 -6x + 3y – 9z = 15 4x – 2y + 6z = -10 2x – 3y – 5z = 27 5x + 7z = 0 -4x – 14z = 42

5x + 7z = 0 -4x – 14z = 42

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 - 7z = -35

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

3.5 – Solving Systems of Equations in Three Variables Ex. x + 2y + z = 10 2x – y + 3z = - 5 2x – 3y – 5z = 27

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 35 + 7z = 0 7z = -35 z = -5

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 7z = -35 z = -5

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 2y + 2 = 10 7z = -35 z = -5

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5 y = 4

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5 y = 4

5x + 7z = 0 -4x – 14z = 42 2[5x + 7z = 0] -4x – 14z = 42 10x + 14z = 0 -4x – 14z = 42 6x = 42 x = 7 5x + 7z = 0 x + 2y + z = 10 5(7) + 7z = 0 7 + 2y – 5 = 10 35 + 7z = 0 2y + 2 = 10 7z = -35 2y = 8 z = -5 y = 4 (7,4,-5)