Question

It is impossible for a system of linear equations to have exactly two solutions. explain why

Answer 1

A linear equation represents a straight line.Thus, the solution of the system of linear equation depends on whether the lines intersect, not intersect or same line.

We have below cases:-

• The lines are non parallel and intersect at exactly one point. In this case we have one solution.
• The lines are parallel and hence never intersect. There is no solution in this case.
• The two lines represents the same line. Hence, infinitely many solutions.

We never got exactly two solutions because two lines can intersect at a single point.