what are some methods of solving systems of linear equations

graphing

tabulation
substitution
elimination
comparison
Cramer's rule
Gauss methods
inversion
iterations (such as Gauss-Seidel method)

2. Use the linear combination method to solve the following system of equations. Explain each step of your solution.

2x - 3y = 13 and x + 2y = -4

please solve

There are several methods of solving systems of linear equations. Here are a few commonly used methods:

1. Graphical Method: This method involves graphing the equations on a coordinate plane and finding the point where the graphs intersect, which represents the solution to the system. This method is useful when dealing with simple equations and when visualizing the solution is helpful.

2. Substitution Method: In this method, you solve one equation for one variable and substitute the expression into the other equation. By substituting the value of the variable, you can then solve for the other variable. This process is repeated until both variables are determined, resulting in the solution to the system.

3. Elimination Method (also known as the Addition/Subtraction Method): In this method, you manipulate the equations to eliminate one variable by adding or subtracting the equations together. The goal is to create a new equation with only one variable, which can then be solved for. Once one variable is determined, you can substitute its value back into one of the original equations to find the other variable.

4. Matrix Method (or Matrix Algebra): This method involves using matrices and matrix operations to solve systems of equations. The system of equations is represented as a matrix equation, and various matrix operations are utilized to transform the equations into simpler forms until a solution is obtained.

5. Cramer's Rule: Cramer's Rule is a method that uses determinants to solve systems of equations. Each variable's value is determined by evaluating a determinant involving the coefficient matrix and determinants obtained by replacing the column corresponding to each variable with the constant term column.

It's important to note that the best method for solving a particular system of linear equations depends on the specific equations and the desired approach.