Solving Systems of Equations Using Augmented Matrices

Solve, if possible.

4x - 2y = 2

5x - 2y + z = 7

3x + 4y - z = 3

• x = 1, y = 1, z = 4

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Solve, if possible.

x - y + 2z = -1

-3x + 3y + 5z = 3

2x - 2y = -2

• x = 1, y = 1, z = 4

• No solution

• Infinitely many solutions

• x = -1, y = -1, z = 4

2x + 5y + z = -12

-x + 4y + 3z = -4

5x - 2z = -13

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Solve, if possible:

3x + 2y - 3z = 13

4z + 4x = 12

-2x - y + z = 8

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Solve the system of equations using a matrix technique and your GC

• ( 4, 0, -2)

• ( -4, -2, 0)

• None of these

• ( -4, 0, -2)

Solve by matrices.

4x+9y=28

-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

State the dimensions of the augmented matrix for the system.

• 2 x 3

• 3 x 2

• 3 x 4

• 4 x 3

Which system matches the augmented matrix shown?

• 2x+y+2z=2
  3x+5y-z=4
  x-2y-3z=6

• x+y+z=2
  3x-5y-z=4
  x+2y-3x=6

• 2x-2z+y=2
  3x-5y+z=-4
  x-2y-3z=6

• 2x+y+2z=2
  3x-5y-z=4
  x-2y-3z=-6

• a

• b

• c

• d

State the dimensions of the augmented matrix for the system.

• 2 x 3

• 3 x 2

• 3 x 4

• 4 x 3