basic

Two-Line 2-D Intersection Calculator

Solve a₁x + b₁y = c₁ and a₂x + b₂y = c₂.

Compute the (x, y) intersection of two lines a₁·x + b₁·y = c₁ and a₂·x + b₂·y = c₂ via the determinant. Returns the unique point, or flags parallel / coincident lines.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

D = a₁·b₂ − a₂·b₁. If D ≠ 0: x = (c₁·b₂ − c₂·b₁) / D, y = (a₁·c₂ − a₂·c₁) / D.

In depth

Compute the (x, y) intersection of two lines a₁·x + b₁·y = c₁ and a₂·x + b₂·y = c₂ via the determinant. Returns the unique point, or flags parallel / coincident lines.