Find the exact point where two lines cross in 2D space. Solve systems of linear equations graphically and algebraically.
System Equations
Line 1: a₁x + b₁y = c₁
Line 2: a₂x + b₂y = c₂
Geometric Result
(3.00, 2.00)Point
Intersection Point (x, y)
System TypeIntersecting
Determinant-2.00
Intersection Localized
About this calculator
Intersections and Systems
The intersection of two lines represents the common solution to their linear equations. Algebraically, this is solving a system of two equations with two variables. The point (x, y) satisfies both equations simultaneously.
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Pro Tips
Parallel: If the slopes are equal but intercepts differ, there is no intersection.
Coincident: If the lines are identical, they intersect at every point on the line.
Perpendicular: If the product of slopes is -1, they intersect at a right angle.
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Fun Facts
"If the lines are parallel and distinct, it is an 'Inconsistent System'."
"If the lines are the same, it is a 'Dependent System'."
"Linear systems with intersection points are the basis for many algorithms in robotics."
