# 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 $d x + e y = f$

How to use the calculator

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

This calculator solves the
system of equations, represented by the two lines.

2 - press "enter". The answer is a point whose coordinates are x and y.

Note that

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.

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