Point of Intersection of two Lines Calculator
An online calculator to find the point(s) of intersection of two lines given by the equations : \[ a x + b y = c \quad \text{and} \quad d x + e y = f \]
is presented
Intersection of two Lines
The point of intersection of the two lines is found by solving the system of equations
\[
\begin{cases}
ax + by = c \\
dx + ey = f
\end{cases}
\]
This calculator solves the system of equations, represented by the equations of the two lines above using Cramer's rule.
1 - if you enter parameters \( a, b, c, d, e\) and \( f \) such that \( D = a \times e - b \times d \ne 0 \) , one point of intersection exists and is calculated and displayed.
2 - if you enter parameters \( a, b, c, d, e\) and \( f \) such that \( D = a \times e - b \times d =0 \) , two possible cases:
case 1) If either \(D_x = c \times e - b \times f \ne 0 \) or \( D_y = a \times f - c \times d \ne 0 \) , no point of intersection exists. The message "no solutions" is dispalyed.
case 2) If both \(D_x = c \times e - b \times f = 0 \) and \( D_y = a \times f - c \times d = 0 \), 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" to obtain the point of intersection.
Now write equations, solve the system manually and then check your answer against the one given by the calculator.
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