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Intersection of Two Lines Calculator — result sheet
Solve two lines in standard form and report their intersection or parallel status.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For A₁x+B₁y=C₁ and A₂x+B₂y=C₂, Δ=A₁B₂−A₂B₁; x=(C₁B₂−C₂B₁)/Δ and y=(A₁C₂−A₂C₁)/Δ.
The determinant identifies whether the lines meet at one point and the closed-form solution keeps the coefficient convention visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Line 1 coefficient A — minimum -1000000; maximum 1000000
- Line 1 coefficient B — minimum -1000000; maximum 1000000
- Line 1 constant C — minimum -1000000000; maximum 1000000000
- Line 2 coefficient A — minimum -1000000; maximum 1000000
- Line 2 coefficient B — minimum -1000000; maximum 1000000
- Line 2 constant C — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Line 1 coefficient A | 2 |
| Line 1 coefficient B | 1 |
| Line 1 constant C | 8 |
| Line 2 coefficient A | 1 |
| Line 2 coefficient B | -1 |
| Line 2 constant C | 1 |
The lines meet at x = 3, y = 2.
Assumptions and limits
- The two equations are in a common Cartesian coordinate system.
- A zero determinant means parallel or coincident lines and needs a separate consistency check.
- Inputs are treated as exact numbers within floating-point tolerance.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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