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System Equation Solver
Solve simultaneous linear equations in 2 or 3 variables instantly using matrix determinant methods.
Input Matrix [A | B]
x
y
x
y
Current Equation Representation:
1x + 1y = 5
1x + -1y = 1
Solution Output
x value3.00
y value2.00
Mathematical Proof (Cramer's Rule)
1
Determinant (D) = (1 * -1) - (1 * 1) = -2.00
2
Dx = (5 * -1) - (1 * 1) = -6.00
3
Dy = (1 * 1) - (5 * 1) = -4.00
4
x = Dx / D = 3.00
5
y = Dy / D = 2.00
How it works
This solver uses **Cramer's Rule**, a method for solving systems of linear equations using determinants. It calculates the main determinant of the coefficient matrix and then substitute each column with the constant vector to find variable-specific determinants.
Constraints
A system has a unique solution if and only if the determinant is **non-zero**. If the determinant is zero, the system is either inconsistent (no solution) or dependent (infinitely many solutions).