Three Variable Systems Practice

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 (iiI) by 4.

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

• They would multiply equation (i) by 3

For the system of equations:
A:   3x - 2y + 4z =  9
B:   -2x + y - 2z = -8
C:   6x - 4y + 5z = 22
A good option for solving this would be:

• take 2 times A + B to get equation D,
   then take 4 times B + C to get equation E.

• Take  A + 2 times B to get D, then
  take 2 times A + C to get E.

• take 2 times B + A to get D, then
  take -2 times A + C to get E.

• Add A + B + C to get the answer.

What would you solve for First?

• Solve for x

• Solve for y

• Solve for z

• (5,3,4)

How many variables are we using if the solution set is \left(x,\, y,\, z\right)

• 1

• 0

• 3

• 2

What is the solution set of the given system?

• (1,-1, 0)

• The system has no solution.

• (13/4, 1/4, 31/4)

what is the value of s in the system

• s=3

• s=2

• s=1

• s=-1

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 of equations: 

• ( 4, 2, -1)

• ( 4, 3, -1)

• None of these

• ( -4, 3, 1)

How many solutions does the following system of equations have?

• No Solution

• Infinitely Many Solutions

• One Solution

• Cannot Be Determined