Consider the system of linear equation

x_{1} + 2x_{2} + x_{3} = 3

2x_{1} + 3x_{2} + x_{3} = 3

3x_{1} + 5x_{2} + 2x_{3} = 1

The system has

- Infinite no. of solutions
- No solution
- Unique solution
- Exactly 3 solutions

**Solution**

You need to eliminate one variable.

Subtract first equation from the second equation,

(ii) - (i): x_{1} + x_{2} = 0

Multiply second equation by 2 and then subtract third equation from it,

2 x (ii) - (iii): x_{1} + x_{2} = 5

The two lines are parallel, so there is no solution.

**The correct option is B.**