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📘 Class 9 Maths Chapter 4: Linear Equations in Two Variables (Complete Notes)

🔹 Introduction

Linear equations in two variables help us represent relationships between two quantities. In this chapter, we study how to form and solve such equations. Moreover, these equations are useful in daily life problems like cost calculation and distance problems.

🔹 Linear Equation in Two Variables

A linear equation in two variables is an equation of the form:

ax + by + c = 0

Here, x and y are variables, while a, b, and c are constants. Also, a and b cannot be zero at the same time.

👉 Example:
2x + 3y = 6

🔹 Solution of Linear Equation

A solution of a linear equation is a pair of values (x, y) that satisfies the equation.

For example, in the equation 2x + 3y = 6:
If x = 0, then y = 2
If x = 3, then y = 0

Therefore, (0, 2) and (3, 0) are solutions.

🔹 Infinite Solutions

A linear equation in two variables has infinitely many solutions. This happens because we can choose many values of x and find corresponding values of y. Hence, the equation represents a line.

🔹 Graph of Linear Equation

The graph of a linear equation in two variables is always a straight line. To draw the graph, we find at least two solutions and plot them on a coordinate plane. After that, we join the points to form a line.

👉 Example:
For 2x + 3y = 6
Points: (0, 2) and (3, 0)

🔹 Steps to Draw Graph

First, find two or more solutions of the equation. Next, plot these points on the graph paper. Then, join them using a straight line. Finally, extend the line on both sides.

🔹 Equations of Lines Parallel to Axes

Some equations represent lines parallel to axes.

• Equation x = a represents a line parallel to y-axis
• Equation y = b represents a line parallel to x-axis

👉 Example:
x = 2 → vertical line
y = 3 → horizontal line

🔹 Important Observations

Every linear equation in two variables represents a straight line. Also, every point on the line is a solution of the equation. Therefore, graph and equation are closely related.

🔹 Uses of Linear Equations

Linear equations are useful in many real-life situations. For example, they help in calculating costs, distances, and time. Moreover, they are used in business, science, and engineering.

🔹 Important Points

Always write the equation in standard form. Also, find at least two points to draw a graph. In addition, practice graph drawing regularly to improve accuracy. Therefore, regular practice will help in exams.