Systems With Three Variables

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

• the intersection of three planes

• the origin

• infinitely many solutions

• no unique solution

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

• Yes

• No

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)

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

How many solutions are shown in the diagram?

• 0

• 1

• 2

• 3

What variable should I eliminate first in the following system?

• x

• y

• z

Solve the system of equations to find the value of y.

• -2

• 3

• -3

• 2

Solve the system of equations to find the value of z.

• 4

• -4

• 2

• -2

Solve the system.

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution