How to solve a system of linear equations?

To solve a system of linear equations, one must find the values of the variables that satisfy all the equations simultaneously. There are several methods to accomplish this. One common method is substitution, where one variable is isolated in one equation and then substituted into the other equations. Another method is elimination, where one multiplies the equations by appropriate factors to create equal coefficients for one of the variables, allowing them to cancel each other out when added or subtracted. Additionally, the matrix method can be used, where the coefficients of the variables are arranged in a matrix equation and solved using matrix operations. Regardless of the method used, it is important to check the solution by substituting the values back into the original equations to ensure they satisfy all the given equations.

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