Pair of Linear Equations in Two Variables | Class 10 Mathematics Notes

3.3.2 Elimination Method

This subsection details the elimination method, an algebraic technique to solve pairs of linear equations by eliminating one variable. The process involves multiplying the equations by suitable constants to make the coefficients of one variable equal (or additive inverses), then adding or subtracting the equations to eliminate that variable. This reduces the system to a single-variable equation, which can be solved easily. After finding the value of one variable, substitution back into one of the original equations yields the other variable's value. The section outlines the stepwise procedure: (1) multiply equations to equalize coefficients, (2) add or subtract to eliminate a variable, (3) solve the resulting equation, and (4) substitute back. Examples illustrate solving real-life problems such as income-expenditure ratios and digit-based number puzzles. The method also helps identify inconsistent systems when subtraction leads to false statements and dependent systems when it leads to true statements without variables. The elimination method is often more convenient than substitution, especially when coefficients are easily manipulated.

🧪 Activity: Exercises involving elimination method to solve pairs of linear equations.

🔗 Connection: Leads to understanding conditions for consistency and inconsistency of pairs of linear equations.