Resolvedor de Sistemas de Equacoes Gratis
Resolva sistemas de duas equacoes lineares com duas incognitas. Metodo de substituicao e Cramer com passos.
X Val
1.000000
Formula
## How to Solve Simultaneous Equations ### Cramer's Rule for 2×2 Systems Given: - a₁x + b₁y = c₁ - a₂x + b₂y = c₂ **Determinant D = a₁b₂ - a₂b₁** **x = (c₁b₂ - c₂b₁) / D** **y = (a₁c₂ - a₂c₁) / D** If D = 0, the system has no unique solution (the lines are parallel or identical).
Exemplo Resolvido
Solve: 2x + 3y = 8 and 4x - y = 2.
- 01D = (2)(-1) - (4)(3) = -2 - 12 = -14
- 02x = (8×(-1) - 2×3) / (-14) = (-8 - 6) / (-14) = -14 / -14 = 1
- 03y = (2×2 - 4×8) / (-14) = (4 - 32) / (-14) = -28 / -14 = 2
- 04Solution: x = 1, y = 2
Perguntas Frequentes
What are simultaneous equations?
Simultaneous equations are a set of equations with multiple unknowns that must be solved at the same time. The solution satisfies all equations simultaneously.
When does a 2×2 system have no solution?
When the determinant equals zero. This means the two lines are parallel (no intersection) or identical (infinite solutions).
What is Cramer's rule?
Cramer's rule uses determinants to solve systems of linear equations. For a 2×2 system, each variable is found by taking the ratio of two determinants.
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