Solving Systems of 3 Equations 3 Variables

Learn how to solve systems of three linear equations with three variables using the elimination method! This video will guide you through three detailed examples, showing you a systematic approach to finding the unique solution (x, y, z) that satisfies all three equations. Solving 3x3 systems of equations is a fundamental skill in Algebra 2 and Precalculus. You'll learn how to strategically eliminate one variable to reduce the system to two equations with two variables, then solve that smaller system, and finally use back-substitution to find the values of all three variables. In this video, you'll learn: Setting up the Problem: Understanding what a system of three equations with three variables represents (the intersection point of three planes). Choosing a Variable to Eliminate: Strategies for selecting the easiest variable to eliminate first. First Elimination Step: Combining two pairs of equations to eliminate the same variable, resulting in a 2x2 system. 0:40 Example 1: Eliminating 'Z' from Equation 1 and Equation 2. 2:20 Example 1: Eliminating 'Z' from Equation 2 and Equation 3. Solving the 2x2 System: Using the elimination method again to solve for one variable. 4:00 Example 1: Eliminating 'Y' from the new 2x2 system. Back-Substitution: Working backward to find the values of the other variables. 5:50 Example 1: Solving for 'Y'. 6:40 Example 1: Solving for 'Z'. Writing the Solution: Expressing the answer as an ordered triple (x, y, z). Checking Your Solution: How to verify your answer by plugging it back into the original equations. 7:40 Example 2: Solving another system of 3 equations with 3 variables. 8:30 Eliminating 'Y' from Equation 1 and Equation 3. 9:50 Eliminating 'Y' from Equation 1 and Equation 2. 11:50 Solving the resulting 2x2 system for 'X'. 12:50 Back-substituting to find 'Z'. 14:00 Back-substituting to find 'Y'. 15:00 Writing the solution as an ordered triple. 16:00 Example 3: Solving a third system of 3 equations with 3 variables. 18:00 Eliminating 'X' from Equation 1 and Equation 2. 19:00 Eliminating 'X' from Equation 2 and Equation 3. 20:40 Solving the resulting 2x2 system for 'Z'. 21:50 Back-substituting to find 'Y'. 22:50 Back-substituting to find 'X'. 23:30 Writing the solution as an ordered triple. Master solving systems of three equations with three variables! If you found this video helpful, please give it a thumbs up and subscribe to Mario's Math Tutoring for more algebra and precalculus lessons! #SystemsOfEquations #ThreeVariables #ThreeEquations #EliminationMethod #Algebra #Algebra2 #Precalculus #LinearEquations #MathTutorial #MathHelp #MarioMathTutoring ➡️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