2×2 Linear System
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Tap a term to see what it means, or .
Calculate
Example: two coffees and a bread roll cost 7, and a coffee costs 1 less than a roll. With x the coffee and y the roll: 2x + y = 7 and x − y = −1. How much is each? Change the coefficients to solve your own system a·x + b·y = c.
Step by step
What each term means
- Unknown x
- The first value sought. Geometrically, the x coordinate of the point where the two lines cross.
- Determinant Dₓ
- The determinant of the coefficients with the x column replaced by the constants c₁ and c₂.
- Determinant D
- The determinant of the coefficients, a₁b₂ − a₂b₁. Zero means parallel lines: no solution, or infinitely many.
- Unknown y
- The second value sought, the y coordinate of the crossing.
- Determinant D_y
- The determinant with the y column replaced by the constants.