Solve
3x – y + 2z = 6
-x + y = 2
x – 2z = -5

Step-by-step explanation:

3x – y + 2z = 6 - - - - - - - - - 1

-x + y = 2 - - - - - - - - - - - - -2

x – 2z = -5 - - - - - - - - - - - -3

From equation 2, x = y - 2

From equation 3, x = 2z - 5

Substituting x = y - 2 and x = 2z - 5 into equation 1, it becomes

3(y - 2) – y + 2z = 6

3y - 6 - y + 2z = 6

3y - y + 2z = 6 + 6

2y + 2z = 12 - - - - - - - - - 4

3(2z - 5) – y + 2z = 6

6z - 15 - y + 2z = 6

- y + 6z + 2z = 6 + 15

- y + 8z = 21 - - - - - - - - - - 5

Multiplying equation 4 by 1 and equation 5 by 2, it becomes

2y + 2z = 12

- 2y + 16z = 42

Adding both equations

18z = 54

z = 54/18 = 3

Substituting z = 3 into equation 5, it becomes

- y + 8×3 = 21

- y + 24 = 21

- y = 21 - 24 = - 3

y = 3

Substituting y = 3 into equation 2, it becomes

-x + 3 = 2

- x = 2 - 3 = -1

x = 1

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