System of Equations in Three Variables

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

The solution to a 3-variable systems of equation is...

• the intersection of three planes

• the origin

• infinitely many solutions

• no unique solution

Solve the system.

• (1, 2, -5)

• (1, -2, 5)

• (2, -4, -5)

• (3, 1, -5)

Is (4,5,6) a solution to 2x-3y+z=8

• Yes

• No

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

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

• No solution

• Infinitely many solutions

• All real numbers

• (x,y,z)

Tags

CCSS.8.EE.C.7A

A student in solving the following system of equations using the elimination method. Explain what their first step would be if they wanted to eliminate the y variable from equations (i) and (ii).

• They would multiply equation (i) by 3 and equation (ii) by 4.

• They would multiply equation (ii) by 4.

• They would multiply equation (i) by -3 and multiply equation (ii) by 4

• They would multiply equation (i) by 3