Simultaneous Equations Solver (2×2)
Solve a system of two linear equations with two unknowns using Cramer's rule. Enter coefficients for a1*x + b1*y = c1 and a2*x + b2*y = c2.
X Val
1.000000
सूत्र
## 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).
हल किया गया उदाहरण
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
अक्सर पूछे जाने वाले प्रश्न
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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