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📘 Class 9 Maths Chapter 4 – Linear Equations in Two Variables | Full Chapter Summary

In this chapter, "Linear Equations in Two Variables", we explore equations that involve two variables and understand how they can be represented on a graph. This chapter connects algebra with geometry and helps in solving many real-life problems.


🔹 1. Introduction to Linear Equations

A linear equation in two variables is an equation of the form:
ax + by + c = 0
where a, b, c are real numbers and a, b ≠ 0.


🔹 2. Solution of a Linear Equation in Two Variables

Any ordered pair (x, y) that satisfies the equation is called its solution.

A linear equation in two variables has infinitely many solutions.


🔹 3. Graphical Representation

The graph of a linear equation in two variables is always a straight line.

Each point on the line corresponds to a solution of the equation.


🔹 4. Steps to Plot a Linear Equation on the Graph

Rewrite the given equation in standard form.

Find at least two (x, y) solutions.

Plot these points on the coordinate plane.

Join them to get a straight line.


🔹 5. Examples of Linear Equations

x + y = 10

2x – 3y + 6 = 0

3x + 2y = 12


🔹 6. Applications of Linear Equations in Two Variables

Representing real-life problems like:

Age-related problems

Money and cost problems

Geometry-based questions

Used to find relationships between quantities.


🎯 Key Learning Outcomes

Understanding the structure of linear equations.

Learning to find infinite solutions.

Representing equations graphically as straight lines.

Applying concepts to real-life problem solving.


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