System of Equations Calculator
System of equations calculator
Solve a 2x2 linear system of equations with unique solution.
InputsForm6 fieldsLive
Result
x = 2, y = 1
Solved using determinant method (Cramer-style).
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Formula
Delta = a1b2 - a2b1 x = (c1b2 - c2b1)/Delta y = (a1c2 - a2c1)/Delta Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
a_1, b_1, c_1 | Coefficients of first equation a1x + b1y = c1 | number | |
a_2, b_2, c_2 | Coefficients of second equation a2x + b2y = c2 | number | |
\Delta | Determinant (must be non-zero for unique solution) | number |
- Compute determinant Delta from coefficient matrix.
- If Delta is zero, the system has no unique solution.
- Otherwise compute x and y with determinant ratios.
Example
Worked example: 2x + y = 5 and x - y = 1
- 1 Delta = 2(-1) - 1(1) = -3
- 2 x = (5(-1) - 1(1))/(-3) = 2
- 3 y = (2(1) - 1(5))/(-3) = 1
The unique solution is x = 2, y = 1.
How
- Enter coefficients a1, b1, c1 for the first equation.
- Enter coefficients a2, b2, c2 for the second equation.
- Read the solved x and y values instantly.
Avoid
- Entering equation constants on the wrong side without sign adjustment.
- Ignoring the Delta = 0 case where unique solution does not exist.
- Swapping coefficient positions between equations.
FAQ
What happens when determinant is zero?
The system has either infinitely many solutions or none, so there is no unique x,y pair.
Can this solve 3-variable systems?
No, this version is specifically for 2 equations with 2 unknowns.
Can coefficients be decimals?
Yes, decimal and negative coefficients are supported.
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