Systems of Linear Equations

Consider the system of linear equations composed of the following lines: 

y = 3x - 7
y = 5x - 8

The solution to this system of linear equations is the point where the two lines intersect.  

In this section, we cover three methods for determining the solution to a system of linear equations: 

• Graphing
  • A handy tool for graphing is Desmos Graphing
• Substitution
• Elimination  

While the examples shown here are for systems of linear equations that only have two variables, there are techniques that can be applied to more complex linear systems with more than two variables.  

The following document contains the complete transcript and notes for the videos below: 

In this first video, the graphing and substitution methods for solving a system of linear equations are demonstrated.

This second video provides a detailed explanation of the elimination method for solving systems of linear equations. Additionally, it showcases a couple of practical applications of this method in a real-world scenario.