# Point of Intersection of two Lines Calculator

An online calculator to find the point(s) of intersection of two lines given by the equations :

a x + b y = c

and

d x + e y = f .

## Intersection of two Lines

This calculator solves the system of equations , represented by the two lines above.1 - if you enter parameters a, b, c, d, e and f such that D = a*e - b*d is not equal to zero, one point of intersection exists and is calculated and displayed.

2 - if you enter parameters a, b, c, d, e and f such that D = a*e - b*d = 0, two possible cases:

case 1) If either Dx = c*e - b*d is not equal to zero or Dy = c*e - b*d is not equal to zero, no intersection exists. The message "no solutions" is dispalyed.

case 2) If both Dx = c*e - b*f = 0 and Dy = a*f - c*d = 0, the two lines are equivalent and have an infinite number of points of intersection given by the graph of one of the two equations.