Solve a system of linear equations (2x2 or 3x3) using determinants.
System Configuration
x +
y=
x +
y=
Solution
Determinant (D)-7.000
x =2.0000
y =3.0000
Cramer's Rule
Cramer's Rule is a method for solving linear systems where the number of equations equals the number of variables. It uses determinants to find the unique solution. If the main determinant is zero, the rule cannot be applied (no unique solution).
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Pro Tips
D is the determinant of the coefficient matrix.
Dx is the determinant formed by replacing the x-column with the constants vector.
Computationally expensive for large systems (n > 3) compared to Gaussian elimination.
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Fun Facts
"Named after Gabriel Cramer (1750), although Colin Maclaurin published similar results earlier."
"It provides an explicit formula for the solution, which is useful in theoretical proofs."
