Systems of Equations with Three Variables

Solve the system.

• (3, -2, 4)
• (2, -3, 1)
• (-3, 2, -1)
• Infinitely many solutions

Solve the system.

• (2, -2, 3)
• (2, 1, 4)
• (-2, 2, -3)
• No Solution

Solve the system. 

• (5, -6, 3)
• (2, 3, -1)
• (-4, 2, 5)
• No Solution

The solution of a system of three linear equations in three variables, x,y, and z, is called a(n) ___________________ (x,y,z).

• Ordered Pair
• Integer
• Ordered Triple
• Sum

Determine which ordered triple is a solution of the systems of equations?
2x+y=0
x+3y-z=-11
7x+5y+4z=21

• (0,0,11)
• (1,-2,6)
• (-1,2,-16
• (0,1,-14)

Solve the system of equations.
x-3y=13
5x+6z=41
2x+4y-z=5

• (7,-2,1)
• (13,0,-4)
• (10,-1,11)
• (1,-4,6)

Solve for x, y and z.

• (2, 5, 6)
• (6, 5, 2)
• (2, 6, 5)
• (6, 2, 5)

Solve the system of equations: 

• ( -2, 3, -3)
• None of these
• ( -2, -3, 3)
• ( -3, 3, -2)

What is your solution if your variables go away and you are left with 0 = 0?

• No Solution
• All Real Numbers
• Infinitely Many Solutions
• (x, y, z)