Linear equations (three variables)

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

Solve the following System --your answer should be in the form: (x,y,z) NO SPACES unless "no solution" or "infinitely many solutions" typed how you see it without quotations.

 $3x-y=11$  

 $2y+z=17$  

 $x+4z=41$  

Solve the System.

• ( -2, 3, -3)

• None of these

• ( -2, -3, 3)

• ( -3, 3, -2)

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.

• x

• y

• z

x+y+z=12

3x+y=19

5x=25

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

Solve the system of equation using the elimination method.

• (0,3)

• (-7,2)

• (2,4)

• (2,2)

Answer explanation

The correct answer is (2,2).

Use your graphic organizer or ask for help if you have additional questions.

What is the first step in solving a system of equations with three variables?

• Solve for the two remaining variables.

• Use the two solutions to find the third variable.

• Eliminate one variable using two pairs of the equations.

Find the solution to the system of equations using Gaussian elimination: 4x - 2y + 3z = 10; 2x + 5y - z = 3; x - 3y + 2z = 1

• x = 2, y = -1, z = 4

• x = 8.4, y = -5, z = -11.2

• x = 5, y = 2, z = -3

• x = -1, y = 3, z = 2