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