Linear Equations

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

  1. Infinite no. of solutions
  2. No solution
  3. Unique solution
  4. Exactly 3 solutions

Solution

You need to eliminate one variable.

Subtract first equation from the second equation,

(ii) - (i): x1 + x2 = 0

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

2 x (ii) - (iii): x1 + x2 = 5

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

The correct option is B.