Crammer rule example
Cramer's rule is a method of solving a system of linear equations by calculating the determinants of matrices. It can be used for systems with 2 or 3 variables, but can be computationally expensive for larger systems.
Here is an example of using Cramer's rule to solve a system of 2 equations with 2 variables:
x + 2y = 5
3x – y = 7
step:
Write the system in matrix form:
| 1 2 | X | 5 |
| 3 -1 | Y | 7 |
Calculate the determinant of the coefficient matrix (Δ):
Δ = | 1 2 | = (1)(-1) - (2)(3) = -7
Replace each variable column with a constant from the right side of the equation and calculate the determinants (Δx and Δy):
Δx = | 5 2 | = (5)(-1) - (2)(7) = -19
Δy = | 1 5 | = (1)(7) – (2)(3) = 1
Solve for the variables:
x = Δx / Δ = -19 / -7 = 2.71
y = Δy / Δ = 1 / -7 = -0.14
Therefore, the solution of the system is x = 2.71 and y = -0.14.
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