免费联立方程组求解器
求解二元一次方程组，显示消元法计算步骤。
X Val
1.000000
公式
## 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).
计算示例
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
常见问题
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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