
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.
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.
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