Simultaneous Equations Explained | Elimination vs Substitution

Simultaneous equations help us solve problems where two unknown quantities must satisfy two relationships at the same time. In this beginner-friendly Business Mathematics lesson, we solve simultaneous equations step by step using both elimination and substitution. You’ll learn: • Why two unknowns usually require two equations • What simultaneous equations mean • How to define two variables • How to build a system of equations • How the elimination method works • How the substitution method works • How to choose between elimination and substitution • How to find both unknown values • How to verify the solution in both original equations • Why both methods lead to the same answer In our worked example: x + y = 190 2x + 3y = 410 where: x = price of the premium add-on y = price of the basic add-on Using elimination, we find: y = 30 Then: x = 160 So: Premium add-on = $160 Basic add-on = $30 We then solve the same system again using substitution and reach exactly the same answer. Elimination is often useful when coefficients can be matched easily. Substitution is often useful when one variable is already isolated or easy to isolate. Neither method is always better. The goal is to choose the method that creates the least unnecessary work. Most importantly, a valid solution must satisfy BOTH original equations. This lesson is part of the *Business Mathematics Made Simple* series from The Student Desk Academy. 📚 Extra practice: Gupta, Problems and Solutions in Business Mathematics and Statistics (2020). ▶️ Next lesson: *Ratios, Rates & Proportions Explained | Business Math Made Simple* Subscribe and continue through the full Business Mathematics series. *The Student Desk Academy* Where complex concepts become simple. #SimultaneousEquations #EliminationMethod #SubstitutionMethod #BusinessMathematics #Algebra