Linear Equations in Two Variables Class 9 Important Questions Free PDF Download

Are you gearing up for your exams and feeling a bit overwhelmed by the topic of Linear Equations in Two Variables? Don’t worry—you’re not alone! Chapter 4 of Class 9 CBSE Maths is a crucial chapter that lays the groundwork for advanced concepts in algebra and geometry. Understanding it is not just important for exams but also for real-world problem-solving skills.

In this chapter, you explore equations like ax+by+c=0, learn how to solve them, and discover how to represent their solutions graphically. With questions ranging from simple computations to real-life applications, this chapter challenges your analytical and reasoning skills.

To help you excel, we’ve curated a list of Linear Equations Class 9 Extra Questions covering all the essential topics, including:

• How to find solutions to linear equations.
• Plotting graphs for linear equations.
• Real-life application-based problems.
• Questions involving intercepts and slopes.

These questions will not only strengthen your conceptual understanding but also boost your confidence to tackle exams. So, let’s dive into this treasure trove of practice questions and master the art of solving Linear Equations in Two Variables with ease!

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Chapter 4 Linear Equations In Two Variables Important Questions

1. A soap manufacturer makes fragrant and non-fragrant liquid soaps. The liquid soaps are filled in plastic bottles and packed in equal size cartons for transportation. Each carton contains 50 bottles. The mass of a full bottle of soap is 220 gm and that of a half-filled bottle is 120 gm. What will be the mass (gm) of the empty bottle?

a. 10

b. 20

c. 100 

d. 110

Solutions:

‍(b) 20

Explanations:

Let the mass of the empty bottle be x gm, and let the mass of the soap in a full bottle be y gm. We will solve this using linear equations in two variables based on the given data:

The mass of a full bottle is 220 gm.

x+y=220                         —-(1)

The mass of a half-filled bottle is 120 gm

x+ y/2 =120                     —--(2)

From Equation (1):

x+y=220

⟹ y=220−x

Substitute y=220−x into Equation (2):

x + (220−x/2)=120

x + (110−x/2)=120

(2x/2)-(x/2)+110=120

(x/2)+110=120

(x/2)= 10

x=20

y=220−20=200

The mass of the empty bottle is 20 gm

The mass of the soap in a full bottle is 200 gm.

2. A carton is checked randomly. Which of the following cannot be the number of fragrant and non-fragrant liquid bottles in the carton?

a. (5, 45) 

b. (15, 35)

c. (20, 30)

d. (30, 40) 

Solutions:

‍(d) (30,40)

Explanations:

Equation x+y=50

Substituting the values of x and y

(5, 45):
Total bottles = 5+45=50
This satisfies the condition.

(15, 35):
Total bottles = 15+35=50
This satisfies the condition.

(20, 30):
Total bottles = 20+30=50
This satisfies the condition.

(30, 40):
Total bottles = 30+40=70
This does not satisfy the condition.

3. The soap bottles are available in small and large sizes. A carton with 10 small and 40 large bottles weighs 10.8 kg. What is the mass of the carton with 50 large bottles?

Solutions:

Let the mass of a small bottle be x kg and the mass of a large bottle be y kg. Using the given data, we will solve the problem using linear equations in two variables.

A carton with 10 small bottles and 40 large bottles weighs 10.8 kg

10x+40y=10.8     —-----------(1)

We need to find the mass of a carton with 50 large bottles, i.e., the value of 50y

10x+40y=10.8 

x+4y=1.08 (Divide by 10) —-----------(2)

From Equation (2), express xxx in terms of y:

x=1.08−4y

When a carton contains 50 large bottles, its weight is:

50y

Thus, we need the value of y. Since we only have one equation, we cannot solve for both xxx and y unless more information is provided about either the mass of the small bottles or the large bottles individually.

4. A carton contains both fragrant and non-fragrant liquid soap bottles. Write an equation representing the number of fragrant and non-fragrant bottles in the carton.

Solutions:

x+y=50

Chapter 4 Linear Equations In Two Variables: Concepts

A linear equation in two variables is an equation that can be written in the form ax+by+c=0 where a, b, and c are real numbers, and a and b are not both zero.

Key Points:

Variables

The equation involves two variables, usually x and y.

Solutions

Any values of x and y that satisfy the equation are called solutions. These solutions can be represented as ordered pairs like (x,y)

Graphical Representation:

A linear equation in two variables is represented by a straight line on a graph.

Every point on the line is a solution to the equation.

The graph can extend infinitely in both directions.

Finding Solutions:

To find solutions, assign a value to one variable and solve for the other. For example, if 2x+3y=6, let x=0 then y=2. This gives the solution (0,2).

Intercepts:

The x-intercept is the point where the line crosses the x-axis (y=0).

The y-intercept is the point where the line crosses the y-axis (x=0).

Real-Life Examples: Linear equations are useful in real life for solving problems related to speed, distance, cost, and other relationships between two quantities.

Steps to Graph a Linear Equation:

Rewrite the equation in the form y=mx+c, if possible.

Identify the intercepts by setting x=0 and y=0.

Plot the intercepts or any two solutions on the graph.

Draw a straight line through the points.

Chapter 4 Linear Equations In Two Variables Important Questions: Why

Practising important questions from Chapter 4: Linear Equations in Two Variables is essential for several reasons. Here’s why this topic deserves your focus:

Core Concept for Algebra: This chapter forms the foundation for advanced topics in algebra and geometry. Mastering it ensures a smoother transition to solving equations with higher complexity in future classes.

Exam Relevance: Questions from this chapter are commonly featured in exams, often carrying significant weightage. Practising important problems helps you become familiar with different types of questions, boosting your confidence.

Graphical Understanding: Linear equations require not just algebraic solutions but also graphical representation. Solving questions helps you develop the skill of plotting graphs accurately and interpreting their meaning.

Real-Life Applications: Many real-world problems involve relationships between two variables, like cost and quantity or speed and time. By practising these questions, you enhance your problem-solving skills, which are valuable beyond academics.

Improved Accuracy and Speed: Solving important questions regularly enhances your accuracy and speed, enabling you to tackle questions quickly and correctly during exams.

Variety of Problems: This chapter includes a mix of conceptual, application-based, and graphical questions. Practising them ensures you’re prepared for all types of problems.

In short, focusing on important questions from this chapter ensures a strong foundation, excellent exam performance, and improved logical thinking. Ready to dive in? Let’s start practicing!

Chapter 4 Linear Equations In Two Variables Important Questions: How

Tackling important questions from Chapter 4 requires a structured and systematic approach. Here’s a step-by-step guide to help you prepare effectively:

Understand the Basics

Start by thoroughly understanding the concept of linear equations in two variables: ax+by+c=0, where a, b, and c are constants.

Familiarise yourself with key terms like solution, x-intercept, y-intercept, and graphical representation.

Master the Formula and Methods

Learn how to:

• Find solutions for a linear equation.
• Convert equations into standard form.
• Plot graphs using at least two points.

Revise the formula y=mx+c, where mmm is the slope and c is the y-intercept.

Practice Graphical Representation

Use graph paper to plot equations and visually understand how solutions form a straight line.

Practice questions involving real-world scenarios, such as speed-time or cost-quantity relationships.

Solve Step-by-Step

Read the question carefully to understand what’s being asked.

If the question involves a graph, identify at least two solutions (ordered pairs) for the equation and plot them accurately.

For word problems, identify the variables and construct the equation before solving.

Focus on Application-Based Questions

Practice questions that apply linear equations to real-life problems, like:

Calculating costs or profits.

Solving distance-speed-time problems.

Determining relationships between two measurable quantities.

Use Sample and Previous Year Questions

Solve sample papers, CBSE question banks, and previous years’ exam questions to understand patterns and frequently asked questions.

Focus on questions with varying difficulty levels, from simple plotting to complex applications.

Revise and Clarify Doubts

Regularly review mistakes to avoid repeating them.

Seek help from teachers, peers, or resources like NCERT solutions if you encounter challenging problems.

Time Your Practice

During preparation, simulate exam conditions by timing yourself while solving questions.

This will help you manage time effectively during the actual exam.

By following these steps, you’ll develop a strong grasp of the topic and gain the confidence to solve any question related to Linear Equations in Two Variables. Keep practising and stay consistent—you’ve got this! We hope that you practice the above Linear Equations Class 9 Extra Questions and achieve your dream marks.

All the Best!