Enter coefficients for both lines and inspect geometry. View intersection type, determinant, and plotted relationship. Download clean reports, tables, and visuals after solving instantly.
Use standard form for each line: Ax + By = C.
| Example | Line 1 | Line 2 | Relationship | Intersection |
|---|---|---|---|---|
| 1 | 2x + 3y = 12 | x - y = 1 | Unique | (3, 2) |
| 2 | 2x + 4y = 8 | x + 2y = 4 | Coincident | Infinitely many |
| 3 | x + y = 5 | 2x + 2y = 8 | Parallel | No intersection |
Each line is entered in standard form: A₁x + B₁y = C₁ and A₂x + B₂y = C₂.
The determinant is D = A₁B₂ − A₂B₁. This value decides whether one solution, no solution, or infinitely many solutions exist.
When D is not zero, the calculator uses Cramer’s Rule:
x = (C₁B₂ − C₂B₁) / D
y = (A₁C₂ − A₂C₁) / D
If D = 0 and both Dx and Dy are zero, the lines are coincident. If D = 0 but Dx or Dy is nonzero, the lines are parallel.
The acute angle between lines uses tan(θ) = |(A₁B₂ − A₂B₁) / (A₁A₂ + B₁B₂)|.
Enter the coefficients A, B, and C for the first line.
Enter the coefficients for the second line in the same format.
Choose graph limits so both lines and the possible intersection stay visible.
Select the number of decimal places you want in the output.
Press the calculate button to show the result summary above the form.
Review the relationship, determinant values, intercepts, slopes, angle, and verification residuals.
Use the CSV or PDF buttons to export your final results.
It uses standard form: Ax + By = C. Enter coefficients for both lines exactly as they appear in your problem.
A zero determinant means the lines do not create one unique intersection. They are either parallel or coincident, depending on Dx and Dy.
Yes. A vertical line appears when B equals zero. The calculator labels the slope as undefined and still evaluates the intersection correctly.
Those labels appear in special cases, such as lines parallel to an axis or lines that lie directly on an axis.
It checks how closely the computed point satisfies each equation. Values near zero confirm the displayed intersection is numerically consistent.
The angle is computed from the line coefficients using a determinant-based tangent formula. This avoids issues with undefined slopes for vertical lines.
Yes. The CSV button downloads the numerical summary. The PDF button captures the visible result section, including the graph.
That entry is not a valid line. The calculator reports invalid input because the equation does not represent a geometric line.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.