The solution of the system of equations 3x + 2y - 6z = 1, 2x - 3y + 3z = -1, x - 4y + z = -6 is:

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  1. (1, -2, 1)
  2. (1, 1, 2)
  3. (2, 1, 1)
  4. (1, 2, 1)

Answer (Detailed Solution Below)

Option 4 : (1, 2, 1)
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Detailed Solution

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Given:

The system of equations 3x + 2y - 6z = 1, 2x - 3y + 3z = -1, x - 4y + z = -6

Concept:

Use concept of elimination of variables.

Calculation:

The system of equations

3x + 2y - 6z = 1 

2x - 3y + 3z = -1

x - 4y + z = -6

Isolate x for 3x + 2y - 6z = 1 :

Now substitute in other equations 

 and

After simplification

 and 

Now, isolate y for 

Now substitute in other equation

 

 

⇒ z = 1

For 

substitute z = 1

 ⇒ y = 2

For  

substitute z = 1, y = 2

 ⇒ x = 1

The solution to the system of equations are:

x = 1, y = 2, z = 1

Hence the option (4) is correct.

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