3.5 – Solving Systems of Equations in Three Variables

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)