Systems of 3 Variable Equations

Vocabulary/Steps

100

The solution to a system of 3 variable equations written as (x,y,z)

Ordered Triple

200

A system of 3 equations in 3 variables x, y, and z

Systems of 3 Variable Equations

300

The method used to cancel variables

Elimination

400

In the system: 

x-2y+3z=7

    y+z=4

   -2z=-10, you solved for z=5. What is the next step?

Plug in z=5 to y+z=4 to solve for y.

Fill In the Blank

100

Systems of 3 variable equations are graphed on a _____________. 

3D Plane

200

If you obtain a false statement, such as 0=1, in any of the steps while solving a system of 3 variable equations, the system has ____    _________.

No Solution

300

• If you obtain a true statement, such as 0=0, in any of the steps while solving a system of 3 variable equations, the system has _________    ________    __________. 

Infinitely Many Solutions

400

You can eliminate a variable by _________ or ________ two equations.

Adding or Subtracting

Checking Solutions

100

Check if (0,1,2) is a solution to the system: 

2x+4y-z=-3

    y+z=4

    2y=-2

NOT a solution

2=-3

3=4

2=-2

200

Check if (2,-2,3) is a solution to the system: 

4x+2y-z=1

x-3y+2z=14

-x+y+z=-1

Yes, it is a solution.

1=1

14=14

-1=-1

300

Check if (0,0,4) is a solution to the system:

2x-2y+6z=10

2x+y+z=10

2x+2y-2z=10

NOT a solution.

20=10

4=10

-8=10

400

Check if (3,−2,1) is a solution to the system:

x+y+z=2

6x−4y+5z=31

5x+2y+2z=13

Yes, it is a solution.

2=2

31=31

13=13

Solving Systems

100

Solve:

x+y+z=10

x+y+z=5

2x+2y+3z=6

No Solution

200

Solve: 

5x+2y-2z=4

    y+2z=10

       5y=-10

(4,-2,6)

300

Solve:

2x+2y+4z=8

2x+2y+4z=8

x+3y+2z=4

Infinitely Many Solutions

400

Solve: 

x+y-3z=-10

x-y+2z=3

2x+y-z=-6

(-2,1,3)