Systems of Equations Calculator
Solve a 2x2 linear system.
Scratchpad (not saved)
Save to create a persistent, shareable workspace.
What This Calculator Does
Solve a 2x2 linear system.
It combines a1, b1, c1, a2 to estimate x, y, Determinant.
Formula & Method
Core equations: 2x2 system solved by elimination/Cramer: x=\frac{c_1b_2-c_2b_1}{a_1b_2-a_2b_1},\ y=\frac{a_1c_2-a_2c_1}{a_1b_2-a_2b_1}.
Notation used in the formulas: R = x; x_{1} = a1; x_{2} = b1; x_{3} = c1; x_{4} = a2; x_{5} = b2; x_{6} = c2.
Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.
Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.
Inputs Used
- a1: Used directly in the calculation.
- b1: Used directly in the calculation.
- c1: Used directly in the calculation.
- a2: Used directly in the calculation.
- b2: Used directly in the calculation.
- c2: Used directly in the calculation.
Related Calculators
- Percentage Calculator — Perform common percentage operations: find a percentage of a value, calculate what percentage one number is of another, and find percentage change.
- Fraction Calculator — Add, subtract, multiply, or divide two fractions and simplify the result.
- Ratio Calculator — Simplify a ratio and compute equivalent forms.
- Proportion Calculator — Solve proportions of the form a / b = c / x.
- Average Calculator — Compute mean, median, and mode from up to five values.
- Standard Deviation Calculator — Compute population and sample standard deviation from up to five values.
- Prime Factorization Calculator — Factor an integer and derive divisor-count, divisor-sum, Euler totient, and divisor list.
- GCD / LCM Calculator — Compute greatest common divisor and least common multiple of two integers.