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

Solve, if possible.

3x + 3y = -12

-4x - 2y + 2z = -14

x + 3y + 2z = 11

• x = 1, y = 1, z = 4

• No solution

• Infinitely many solutions

• x = -1, y = -1, z = 4

Solve, if possible.

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, if possible:

-2x - 4y + 4z = 14

4x + 2y + 4z = -4

x + 2z = -2

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1