Question

A system of two linear equations has no solution. How is this possible?

Answer 1

Linear equation when graphed will be a straight line.
If two straight lines are parallel, they will not intersect and so there is no (x,y) point that will lie on both lines. Therefore, there will be no solutions.

Example: y = 3x + 5; y = 3x + 7 or 3x - y = -5 and 3x - y = -7 are two linear equations with no solution.

Answer 2

A System of equations can have:
1. One Solution - if the 2 lines intersect at One point
2. No Solution - if the 2 lines are parallel(No Common Points for the 2 lines)
3. Infinite Solutions - if the 2 lines coincide