Solving Systems of Equation with row operations

Question

3x - y + 5z = 14

2x + 3y + 4z = 7

x + y + z = 2

Answer 1

3x - y + 5z = 14

2x + 3y + 4z = 7

x + y + z = 2

1:[3 -1 5| 14]

2:[2 3 4| 7]

3:[1 1 1| 2]

1) Switch Rows 1 and 3.

2) -3R1 + R3 = R3

3) -2R1 + R2 = R2

4) 4R2 + R3 = R3

5) (1/10)R3 = R3

6) R1 - R2 = R1

7) R1 + R3 = R1

8) -2R3 + R2 = R2

1:[1 0 0| 1]

2:[0 1 0| -1]

3:[0 0 1| 2]

The solutions are x = 1, y = -1, and z = 2. The solution point is (1, -1, 2).