There are several methods for solving a system of linear equations:
1. Graphing method: Plotting the equations on a coordinate plane and finding the point(s) of intersection.
2. Substitution method: Solving one equation for one variable and substituting it into the other equation to solve for the remaining variable.
3. Elimination method: Adding or subtracting the equations in a way that eliminates one variable, then solving for the remaining variable.
4. Matrix method: Representing the system of equations as a matrix, then using matrix operations to solve for the variables.
5. Cramer's rule: Using determinants to solve for the variables in the system of equations.
6. Gaussian elimination: Using a sequence of elementary row operations to transform the augmented matrix of the system into row-echelon form, and then back-substituting to find the values of the variables.
7. Gauss-Jordan elimination: Similar to Gaussian elimination, but the goal is to convert the augmented matrix into reduced row-echelon form, resulting in a solution with unique values for the variables.
These methods can be used individually or in combination depending on the specific characteristics of the system of equations.
What are the methods of solving a system of linear equations?
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