 # 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 equations of 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.

## How to use the calculator to Find the Intersection of two Lines?

1 - Enter parameters a, b and c, of the equation of the first line and parameters d, e and f of the equation of second line and press "enter".

 a x + b y = c 2.1 $x$ + 3/5 $y$ = -6 d x + e y = f 1/2 $x$ + 2.3 $y$ = 9
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