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

3.3 Algebraic Methods of Solving a Pair of Linear Equations

This section introduces algebraic methods to solve pairs of linear equations, which are more precise than graphical methods especially when solutions are non-integers or irrational numbers. Two primary algebraic methods are discussed: the substitution method and the elimination method. The substitution method involves expressing one variable in terms of the other from one equation and substituting it into the second equation to find the values of variables stepwise. Several examples illustrate the substitution method, including solving equations with fractional and irrational coefficients, and real-life problems such as age-related questions and cost calculations. The elimination method involves manipulating the equations to eliminate one variable by addition or subtraction after making coefficients equal, thereby reducing the system to a single-variable equation. The section explains the stepwise procedure for elimination and provides examples, including checking for consistency or inconsistency of the pair based on the resulting statements. The section emphasizes verification of solutions by substituting back into original equations and discusses how algebraic methods complement graphical methods.

🧪 Activity: Solving real-life problems algebraically using substitution and elimination methods.

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