Calculadora do Método de Eliminação (2×2)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
regra de Cramer: x = (c₁b₂−b₁c₂)/(a₁b₂−b₁a₂), y = (a₁c₂−c₁a₂)/(a₁b₂−b₁a₂)
About this calculator
The Elimination Method Calculator (2×2) solves systems of two linear equations with two unknowns, in the form {a₁x + b₁y = c₁, a₂x + b₂y = c₂}. It uses Cramer's rule, which calculates x and y via determinants. The main determinant is a₁b₂ − b₁a₂. If it is zero, the system may be inconsistent or dependent, and the calculator will alert the user.
Usage is straightforward: enter the coefficients a₁, b₁, c₁ from the first equation and a₂, b₂, c₂ from the second. The calculator then computes x = (c₁b₂ − b₁c₂) / (a₁b₂ − b₁a₂) and y = (a₁c₂ − c₁a₂) / (a₁b₂ − b₁a₂). The result is displayed clearly, as fractions or decimals. This tool is useful for students, teachers, and professionals needing quick system solutions.
Use this calculator when you need to solve intersection points of lines, simple chemical equation balancing, or any situation modeled by two linear equations. For example, find the equilibrium point between supply and demand in economics, or determine currents in simple electrical circuits. It is both educational and practical.
Cautions: ensure equations are in standard form (ax + by = c). If fractions are present, convert to decimals or use a fraction calculator. Remember the method fails if the determinant is zero (no unique solution). In such cases, the calculator will indicate an error. Always double-check entered coefficients to avoid typos.
Frequently asked questions
What does it mean if the calculator's determinant is zero?
If the main determinant (a₁b₂ − b₁a₂) is zero, the system has no unique solution. It may be inconsistent (no solution) or dependent (infinite solutions). The calculator will show an error message.
Can I use this calculator for systems with more than two equations?
No, this calculator is specific to 2×2 systems. For larger systems, you need other methods like Gaussian elimination or inverse matrices.
How do I enter negative or fractional coefficients?
Enter negative numbers with a minus sign (e.g., -3). For fractions, use decimals (e.g., 0.5). The calculator accepts real numbers.
Does the calculator show step-by-step solution?
No, it only displays the final result (x and y values). To learn the method, consult educational materials or use the calculator to check answers.
Can the result be a fraction?
Yes, if coefficients are integers, the result may be a fraction. The calculator displays the decimal value, but you can use a separate fraction calculator to get the exact fractional form.