How do you solve a system of linear equations?

Solving a system of linear equations involves finding the values of the variables that satisfy both equations simultaneously. There are multiple methods to solve such systems, including substitution, elimination, and matrix methods. In substitution, one equation is solved for one variable in terms of the other, and that value is substituted into the other equation. This process continues until the remaining variables are solved. In elimination, the two equations are manipulated so that when adding or subtracting them, one variable is eliminated and the equation can be solved for the other variable. Matrix methods involve representing the system of equations as a matrix and performing row operations to obtain a simplified form where the variables can be determined. Solving systems of linear equations is essential in various fields, including mathematics, physics, engineering, and economics, as it allows for finding solutions to real-world problems.

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