Elimination Method for Solving Systems of Equations Addition & Subtraction

Learn how to solve systems of linear equations using the elimination method! This video provides a clear, step-by-step guide through five different examples, covering various scenarios you might encounter. The elimination method is a powerful algebraic technique to find where two lines intersect by strategically adding or subtracting equations to eliminate one variable. We'll start with basic examples where variables cancel out easily, then move to more complex problems requiring multiplication of one or both equations by a constant. Finally, we'll explore special cases: systems with infinitely many solutions and systems with no solution. In this video, you'll learn: The core concept of the elimination method for systems of equations. How to add equations to eliminate a variable. How to subtract equations to eliminate a variable. Multiplying one equation by a constant to set up elimination. Multiplying both equations by constants to set up elimination. Solving for the remaining variable and back-substituting to find the other. How to check your solutions. Recognizing special cases: infinitely many solutions (identity) and no solution (contradiction). Timestamps: 0:00 Introduction to the Elimination Method for Systems of Equations 0:40 Example 1: Basic Elimination by Addition (Variables cancel directly) 2:20 Checking the Solution for Example 1 2:40 Example 2: Elimination by Subtraction (Same coefficients) 4:20 Checking the Solution for Example 2 4:40 Example 3: Multiplying One Equation to Eliminate a Variable 7:00 Checking the Solution for Example 3 7:20 Example 4: Multiplying Both Equations to Eliminate a Variable 11:00 Checking the Solution for Example 4 11:20 Example 5: Special Case - Infinitely Many Solutions (Identity) 14:00 Special Case: No Solution (Contradiction) 14:30 Conclusion & Next Steps Perfect for Algebra 1 and Algebra 2 students! Like this video, subscribe to Mario's Math Tutoring for more math help, and check out my video courses in the description if you want to dive deeper into algebra topics! #EliminationMethod #SystemsOfEquations #Algebra #Algebra1 #Algebra2 #LinearEquations #MathTutorial #SolvingSystems #MathHelp #HighSchoolMath #SpecialCases ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join