Solving Systems of Linear Equations
You are likely familiar with solving systems of linear equations in the following ways:
Substitution Putting one variable in terms of the other and substituting this into another equation to solve for 1 variable. This works great with 2 equations and 2 unknowns but scales pretty poorly.
Linearity The solution to linear equations can be added together without loss of information. This is often done by multiplying by scalars to get (additive) inverse coefficients for your variables so they cancel and reduce simply. This works due to linearity.
Other ways of solving these equations include:
Graphing The solution to these systems often appear as intersections. If you can find where and how your linear equations intersect, you can describe their solution.
Matrices Since linear algebra also describes the language of matrices, there are many powerful tools you can use to solve larger systems of linear equations using techniques like RREF or Gaussian elimination.