Philip P. answered • 01/07/21

Affordable, Experienced, and Patient Algebra Tutor

The solution to a system of linear equations occurs at the point where the lines intersect. But two lines will never intersect if they are parallel and have different y-intercepts: For example, consider the two equations:

y = 2x + 3

y = 2x + 5

Since the two lines have the same slope (2), they are parallel. If you set them equal, you get:

2x + 3 = 2x + 5

Subtract 2x from both sides and you get:

3 = 5

which is clearly nonsense. So a nonsensical result means the two lines are parallel and never cross so there is no solution to the system of equations.