Pair of Linear Equations in Two Variables

Board: CBSE Class: 10

Chapter Overview

A linear equation in two variables x and y is of the form ax + by + c = 0. A pair of linear equations can be solved graphically (intersecting, parallel, or coincident lines) or algebraically. Algebraic methods: substitution method, elimination method, and cross-multiplication method. Consistency conditions: unique solution if a1/a2 != b1/b2, no solution if a1/a2 = b1/b2 != c1/c2, infinite solutions if a1/a2 = b1/b2 = c1/c2. Word problems from various contexts.

Topics Covered

Linear Equation
Graphical Method
Intersecting Lines
Parallel Lines
Coincident Lines
Substitution Method
Elimination Method
Cross-Multiplication
Consistency Conditions
Word Problems

Key Formulas

a1/b1 != a2/b2 => unique solution

a1/a2 = b1/b2 != c1/c2 => no solution

a1/a2 = b1/b2 = c1/c2 => infinite solutions

x/(b1c2-b2c1) = y/(c1a2-c2a1) = 1/(a1b2-a2b1)

Real-World Applications

Applications: Cost and pricing problems, speed-distance-time, mixture problems, age problems.

Study Tips

Tip: Choose the right method for each problem

Tip: Practice word problems from NCERT

Tip: Check consistency before solving