4. Algebraic Solutions of Linear Systems


1. Solving Systems of Equations Using Substitution

This method involves subsituting y (or x if it is easier) from one equation into the other equation. This simplifies the second equation and we can solve it easily.

Example:

Solve the system

MATH

using substitution.


Answer


2. Solving Systems of Equations Using Elimination

Our aim here is to eliminate one of the variables. It doesn't matter which one - we usually just do the easiest one.

 

Example:

Solve the system using elimination.

MATH


Answer


Later we will see how to solve systems of equations using determinants (okay for paper-based solutions) and matrices (very powerful and the best way to do it on computers).



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