Suppose a system of linear equations is consistent Explain a

Suppose a system of linear equations is consistent. Explain as clearly as you can why there cannot be exactly two solutions.

THIS IS A CALCULUS 4 QUESTION.

Solution

A consistent system can be either Determined or Undetermined .

For Determined consistent system there is always an unique solution. That means only one set of numbers can satisfy equations .

For Undetermined consistent system there can be infinite solutions. That means the equations will be like identity .And will have infinite number of solutions .

Thatswhy there can never be exactly two solutions for any consistent system, either it will be unique or infinite.