Paano Kalkulahin si System of Equations Solver
Ano ang System of Equations Solver?
A system of linear equations is a set of two or more equations with the same variables. The solution is the point(s) where all equations are satisfied simultaneously.
Pormula
General: Ax = b where A is coefficient matrix, x is variable vector, b is constant vector
- A
- coefficient matrix (m × n)
- x
- variable vector (n × 1)
- b
- constant vector (m × 1)
Step-by-Step na Gabay
- 12×2 system: use Cramer's rule or elimination
- 2Determinant det = a₁b₂ − a₂b₁
- 3x = (c₁b₂ − c₂b₁)/det
- 4y = (a₁c₂ − a₂c₁)/det
Mga Nalutas na Halimbawa
Input
2x+3y=13, 4x−y=5
Resulta
x=2, y=3
Input
x+y=5, 2x−y=4
Resulta
x=3, y=2
Mga madalas itanong
How many solutions can a linear system have?
Zero (inconsistent), exactly one (unique), or infinitely many (infinitely many). It depends on rank and consistency.
When is a system inconsistent?
When the equations contradict (e.g., 0 = 1 after reduction). Geometrically: lines/planes don't all meet at a point.
Can I use elimination or substitution for large systems?
Yes, but matrix methods (Gaussian elimination, LU decomposition) are more efficient for computers.
Handa nang kalkulahin? Subukan ang libreng System of Equations Solver Calculator
Subukan ito sa iyong sarili →