Understanding and solving linear equations in three variables

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

• 4

• -4

• 2

• -2

Use elimination or substitution to solve the systems.

• (1, 4, 4)

• (1,- 4, 4)

• (-1, -4, -4)

Check all that apply. Solve the system: $-3x-7y+2z=-5$ 

 $-3x+8y-10z=7$  

 $3x+y+4z=-7$  

• x = 7

• x = -10

• z = -6

• y = -5

• y = -4

Solve the system:

• 
  

  $\left(-1,3,\ -4\right)$
  

• $\left(-1,\ -3,\ 4\right)$

• Infinitely Many Solutions

• No Solution

Solve the system of linear equations.

• (-1, 1, 2)

• (2, 1, -1)

• no solution

• infinitely many solutions

Solve the system:

• $\left(2,\ -1,4\right)$

• $\left(-2,\ -1,\ 4\right)$

• Infinitely Many Solutions

• No Solution

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.

 $4x-y+4z=23$  

 $5x-4z=-23$  

 $2y+z=25$  

Solve the linear system.

4x - 3y + 5z = -19

3x - y - 8z = -21

-2x + y + 3z = 13

• (1, -4, 3)

• (4, -1, -3)

• (-2, -5, -1)

• (-3, 4, 1)

Solve the following system of equations using the Gaussian elimination method: 2x + 3y - z = 7; x - 2y + 2z = -1; 3x + y - 3z = 4

• x = -9/2, y = 47/8, z = 13/8

• x = 2, y = 1, z = -3

• x = 4, y = 2, z = -5

• x = 1, y = 3, z = -2

4) Solve the system of linear equations.

• (1, -3, -4)

• (-1, 3, -4)

• no solution

• infinitely many solutions