Solveur de Système d'Équations Simultanées Gratuit
Résolvez un système de deux équations à deux inconnues. Trouvez les valeurs de x et y qui satisfont les deux équations.
X Val
1.000000
Formule
How to Solve Simultaneous Equations
Cramer's Rule for 2×2 Systems
Given:
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).
Exemple Résolu
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
Questions Fréquentes
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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