Pair of Linear Equations in Two Variables

Introduction

• Chapter 3 (Class 10th Maths)
• Linear Equation: Any polynomial with degree 1.
• Pair of Linear Equations: A group of two equations with two variables.
  • Example: 2x + 3y + 1 = 0

Standard Form

• Standard Form: A1x + B1y + C1 = 0 and A2x + B2y + C2 = 0
  • A1, B1, C1 and A2, B2, C2: Coefficients
  • x, y: Variables

Equation Solving Methods

1. Graphical Method
2. Substitution Method
3. Elimination Method

Graphical Method

• Concept: Compare ratios of coefficients
  • a1/a2 ≠ b1/b2: Intersecting lines (Unique solution)
  • a1/a2 = b1/b2 = c1/c2: Coincident lines (Infinite solutions)
  • a1/a2 = b1/b2 ≠ c1/c2: Parallel lines (No solution)
• Example: Find coordinates and plot on graph.

Substitution Method

• Steps:
  1. Find the value of one variable from one equation.
  2. Substitute in the other equation.
  3. Solve.
• Example: Find value of x and substitute into y.

Elimination Method

• Concept: Eliminate one variable.
• Steps:
  1. Adjust equations to eliminate one variable.
  2. Solve for remaining variable.
  3. Find the value of the other variable.
• Example: Manipulate coefficients to eliminate one variable.

Oswal Gurukul Book Recommendation

• For solved papers from the past 10 years, especially for exam preparation.

Summary

• There are three main methods to solve pair of linear equations.
• Each method has its own steps to follow.
• By solving equations correctly, the values of variables can be found.

This lecture is helpful in thoroughly understanding mathematical concepts and for exam preparation.