Systems of Three Variables

Which of the following is NOT a coefficient of the following equation: 4z+5x-y=0

• 5

• 4

• -1

• 0

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

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)

What is your solution if your variables go away and you are left with 0 = 17?

• No unique solution

• Infinitely many solutions

• No solution

• (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

Solve the system.

• (1, 2, -5)

• (1, -2, 5)

• (2, -4, -5)

• (3, 1, -5)

• x

• y

• z

 $2x+6y+z=13$  
 $\ \ \ \ \ \ 5y-z=1$  
 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3z=-3$  

Which would be a step in solving the system?

•  $z\ =\ 1,\ 5y\ =\ 2$  

•  $z\ =-\ 1,\ 5y\ =\ 2$  

•  $z\ =\ -1,\ 5y\ =\ 0$  

•  $z\ =\ 1,\ 5y\ -\ 0$