मुफ्त युगपत समीकरण सॉल्वर
दो चरों के दो युगपत समीकरण हल करें। गुणांक दर्ज करें और x, y के मान निकालें।
X Val
1.000000
Det-14.0000
सूत्र
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).
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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