Question

Systems of linear equations

Answer 1

A system of linear equations is a set of two or more linear equations involving the same variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations simultaneously.

There are several methods for solving systems of linear equations, including:

1. Graphical method: Plotting the equations on a graph and finding the point of intersection, which represents the solution to the system.

2. Substitution method: Solving one equation for one variable and substituting that expression into the other equations to solve for the remaining variables.

3. Elimination method: Adding or subtracting the equations to eliminate one variable and solve for the remaining variables.

4. Matrix method: Representing the coefficients of the variables in a matrix and using matrix operations to solve for the variables.

Systems of linear equations can have one unique solution, infinite solutions, or no solutions, depending on the nature of the equations. They are commonly used in various fields such as economics, engineering, physics, and computer science to model and analyze real-world situations.