MCPCalc

Systems of Equations Calculator

Solve 2×2 to 4×4 linear systems using Gaussian elimination, Cramer's rule, and matrix inverse method. Step-by-step working shown.

x+y=
x+y=

Solution:

x = 1.928571

y = 2.714286

det(A)-14.000000
ClassificationUnique solution

For symbolic solutions or parametric forms: Continue in CAS 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=c1b2−c2b1a1b2−a2b1, y=a1c2−a2c1a1b2−a2b1x=\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: RR = x; x1x_{1} = a1; x2x_{2} = b1; x3x_{3} = c1; x4x_{4} = a2; x5x_{5} = b2; x6x_{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.

Reference Book

Linear Algebra and Its Applications

David C. Lay, Judi J. McDonald, and Steven R. Lay · Pearson

A standard text for linear systems, matrices, eigenvalues, diagonalization, and matrix factorizations.

View Book

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