Linear Equation System Solver
Solve a system of two linear equations in two unknowns with Cramer's rule.
Description
Solve a system of two linear equations in two unknowns with Cramer's rule.
Solve a system of two linear equations in two unknowns with Cramer's rule.
When to use Linear Equation System Solver
Use this calculator for direct numerical work with the stated polynomial or equation form and for checking a hand-worked solution.
- a1
- Coefficient of x in the first equation.
- b1
- Coefficient of y in the first equation.
- c1
- Right-hand side of the first equation.
- a2
- Coefficient of x in the second equation.
- b2
- Coefficient of y in the second equation.
- c2
- Right-hand side of the second equation.
How the calculation works
The formula below determines the tool output. x: Solution for x. y: Solution for y. Determinant: Determinant a1*b2 - a2*b1 of the coefficient matrix.1
x = (e d − b f)/(a d − b c); y = (a f − e c)/(a d − b c) Limitations and assumptions
Coefficients are evaluated with floating-point arithmetic. Ill-conditioned systems, nearly repeated roots, and coefficients with very different magnitudes can magnify representation error; the result is not a symbolic proof.
Alternative or Complementary approaches
Complement the numerical result by substituting it back into the original expression. Symbolic algebra or higher-precision arithmetic is a better alternative when an exact form or a proof is required.
References
-
Cramer's rule — Wikipedia contributors
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