Solving a Three Variable System of Equations

the coordinates of a point in space OR the solution to a system of equations in three variables x, y, and z

• ordered triple

• vertex

• linear programming

a set of equations with the same variables

• system of equations

• system of inqualities

• consistent system

any of the points of intersection of the graphs of the constraints that determine a feasible region

• vertex

• ordered triple

• bounded region

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

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

How many solutions are shown in the diagram?

• 0

• 1

• 2

• 3

Which would be correctly rewritten to solve the system ?