This lesson introduces systems of linear equations in two variables and methods for finding their solutions. It reviews linear equations, ordered pairs as solutions, and how graphs of lines represent independent, dependent, and inconsistent systems. Both substitution and elimination methods are demonstrated on multiple examples, including word problems and equations with fractions, with attention to identifying the type of solution from the algebraic work and the graph. The Desmos graphing calculator is also used to visualize intersections, overlapping lines, and parallel lines. Desmos Online Graphing Calculator ➡️ 0:00 Lesson Intro 1:33 Example Graphs of Linear Equations 2:30 Steps to Solve Systems of Linear Equations 3:47 Possible Types of Solutions 4:44 Visual Graph of Independent System (One Solution) 5:56 Visual Graph of Dependent System (Infinitely Many Solutions) 7:00 Visual Graph of Inconsistent System (No Solution) 7:46 Example: Substitution Method 15:12 Example: Elimination Method 23:37 Example: Infinitely Many Solutions 32:45 Example: No Solution 39:15 Example: Linear Equations w/Fractions 52:43 Common Mistakes 53:22 Key Takeaways 🎓 I’m Dr. B. I teach math in a clear, steady way that helps close the gap between how many adults learned math and how students learn it today. 🧠 Whether you’re reviewing a skill, supporting your child, or rebuilding confidence, you’ll find explanations that connect the steps to real understanding. ✨ My hope is that each video helps people feel confident in their own understanding, not just in what an AI tool or program can tell them. 💬 Drop any questions in the comments and share with someone who could use the help! Continue the System of Equations & Matrices full lesson series 👉🏽 #SystemsOfEquations #SubstitutionMethod #EliminationMethod #DrBTeachesMath #ClosingTheGap #LearningWithColors #MathConfidence #MathHelp