Class 10 Maths Chapter 3 Pair of Linear Equations Important Questions with Solutions pdf 2026

Hello students we here again for you with next chapter Pair of Linear Equations in Two Variables is one of the most important topics in Class 10 Maths. In this chapter, students learn how to solve two linear equations together and find the values of unknown variables.

This concept is not only useful for exams but also helps in understanding real-life situations such as finding the cost of items, comparing quantities, and solving daily mathematical problems.

In this chapter, a pair of linear equations is represented in the form:

$a_1x + b_1y + c_1 = 0 \quad \text{and} \quad a_2x + b_2y + c_2 = 0$

• Graphical Method
• Substitution Method
• Elimination Method
• Cross Multiplication Method

Each method helps in finding the values of variables $x$ and $y$ in a systematic way.

Also check:

• Class 10 Maths MCQ Questions for Board Exam 2026 – Important Objective Practice Sheet PDF
• Class 10 Maths Chapter 1 Important Questions with Solutions PDF
• Class 10 Maths Important Questions with Solutions 2026 – Most Repeated Board Questions

Board Exam Importance for Class 10 Maths Chapter 3 Pair of Linear Equations Important Questions

This chapter is highly important for CBSE Board Exams. Every year, 2 to 4 questions are asked from this chapter, including both short answer and long answer questions.

Key areas frequently asked in exams include:

• Solving equations using elimination and substitution methods
• Word problems based on real-life situations
• Graph-based questions
• Checking consistency of equations

Practicing this chapter properly can help students score full marks in this section, as most questions follow standard patterns.

Chapter-wise Important Questions PDF download kare (with full solutions)

Important Concepts

What are Linear Equations?

A Linear Equation is an equation in which the highest power of the variable is 1. In simple words, it is an equation that forms a straight line when represented on a graph.

Standard Form of a Linear Equation

$ax + by + c = 0$

Here:

• $x$ and $y$ are variables
• $a$, $b$, and $c$ are constants
• $a$ and $b$ cannot both be zero

Example of Linear Equations

• $2x + 3y = 6$
• $x – y = 4$
• $3x = 9$

All these are linear equations because the power of variables is 1.

Key Features of Linear Equations

• The graph of a linear equation is always a straight line.
• It can have one or two variables.
• It represents a real-life relationship between quantities.

Why is it Important?

Linear equations are the base of this chapter. Once you understand this concept clearly, solving pair of linear equations becomes very easy.

Graphical Method

The Graphical Method is a way to solve a pair of linear equations by drawing their graphs on a coordinate plane.

In this method, each equation is represented as a straight line, and the solution is the point where both lines intersect.

steps to solve linear equation by Graphical method

• Convert both equations into suitable form
• Find at least two points for each equation
• Plot these points on a graph
• Draw straight lines for both equations

The point where the two lines meet is the solution (x, y)

Possible Cases

• Intersecting Lines → One unique solution
• Parallel Lines → No solution
• Coincident Lines → Infinite solutions

Exam Tip

Substitution & Elimination method

Substitution Method

The Substitution Method is used to solve a pair of linear equations by expressing one variable in terms of the other and then substituting it into the second equation.

Steps to Solve

1. Take one equation and express one variable (x or y) in terms of the other
2. Substitute this value into the second equation
3. Solve the new equation to find one variable
4. Substitute back to get the second variable

This method is very useful when one equation is already simple or can be easily converted into a form like:$$x = \text{something} \quad \text{or} \quad y = \text{something}$$

It helps in solving questions quickly with fewer steps.

• Releted:
• Class 10 Maths Chapter 1 Important Questions (Real Numbers) – Most Repeated CBSE Questions with Solutions & PDF 2026
• Best Scholarships and Competitive Exams After Class 10 in 2026 (Complete Guide)
• Class 10 Maths Sample Paper 2023 Hindi Medium Easy PDF Download

Elimination Method

The Elimination Method is used to solve equations by eliminating one variable through addition or subtraction.

Steps to Solve

1. Make the coefficients of one variable equal in both equations
2. Add or subtract the equations to eliminate one variable
3. Solve the resulting equation
4. Substitute the value to find the other variable

This is the most commonly used method in CBSE exams because it is systematic and works well for all types of questions.

Class 10 Maths Chapter 3 Important Questions with Solutions

1 Mark Questions

Question 1

Write a pair of linear equations in two variables.

Answer:

2x+3y=5 , x−y=2

Question 2

Find the value of $k$k if the pair of equations has infinitely many solutions:

2x+ky=4, 4x+2y=8

Answer:

For infinitely many solutions:

Question 3

Check whether the following pair of equations is consistent:

Answer:

All ratios are equal → Infinitely many solutions (Consistent)

Question 4

If the graph of two linear equations is parallel, how many solutions do they have?

Answer: No solution

Question 5

What is the condition for a unique solution?

Answer:

Question 6

Identify the type of solution:
$$$$

Answer:

Parallel lines → No solution (Inconsistent)

Exam Tip

1-mark questions mostly check your basic concepts and formulas, so revise conditions like:

• Unique solution
• No solution
• Infinite solutions

Ye questions easy hote hain, but concept clear hona zaroori hai.

2–3 and 4 Marks Questions

For scoring good marks in Class 10 Maths, students must practice 2–3 and 4 marks questions regularly. These questions test not only your concepts but also your step-by-step presentation, which is very important in CBSE board exams.

In this section, we have prepared a special handwritten PDF notes that includes:

• ✔️ Important 2–3 mark questions
• ✔️ Previous year board questions
• ✔️ 4 mark detailed solutions
• ✔️ Step-by-step explanations in simple language
• ✔️ Easy methods and shortcuts for faster solving

Handwritten Notes Advantage

These notes are specially designed in a handwritten style so that students can easily understand and revise just like classroom learning.

It feels like studying from a teacher’s personal notebook, making concepts more clear and memorable.

CBSE Exam Pattern

The CBSE Class 10 Maths exam is designed to test students’ understanding, application, and problem-solving skills.

Question Paper Structure

• Section A → 1 mark questions (MCQs)
• Section B → 2 mark questions
• Section C → 3 mark questions
• Section D → 4 mark questions
• Section E → Case study based questions

Why You Should Get This PDF?

• Covers most expected board exam questions in 2026
• Helps in improving answer presentation
• Saves time during revision
• Perfect for last-minute preparation

Download Class 10 Maths Chapter 3 Pair of Linear Equations Important Questions pdf 2026

Download our Handwritten Important Questions PDF and boost your board exam preparation.

FAQs

What is a linear equation?
Ans: An equation in which the highest power of the variable is 1.

Write the general form of a linear equation in two variables.
Ans: $ax + by + c = 0$

How many solutions can a pair of linear equations have?
Ans: One, none, or infinitely many.

What type of lines represent equations with no solution?
Ans: Parallel lines.

Solve: $x + y = 5$, $x – y = 1$

Ans: Adding both: $2x = 6 \Rightarrow x = 3$

Substitute: $y = 2$

Check consistency: $2x + 4y = 8$, $x + 2y = 4$

Ans: Ratios equal → Infinitely many solutions

Find value of k for unique solution:
$kx + y = 2$, $2x + 3y = 5$

Ans: Unique solution when coefficients are not proportional $k/2 \ne 1/3$

Exam Tip

Always write:

• Proper steps
• Final answer clearly
• Method name (substitution/elimination)

Practice Unsolved questions (Based on PYQs)

1.Solve the pair of equations using elimination method:
$2x + 3y = 11$ $2x – 3y = 5$

2.Solve using substitution method:
$x + y = 9$, $x = y + 3$

3.Find the value of $k$k for which the pair of equations has infinitely many solutions:
$2x + ky = 6$, $4x + 2y = 12$

4.Check whether the following pair of equations is consistent or inconsistent:
$x + 2y = 4$, $2x + 4y = 10$

5.Solve the following pair of equations: 3x−y=3 , 2x+y=11

6.Solve using elimination method:
$4x + 5y = 9$, $2x + 5y = 3$

7.Find the solution graphically:

x+y=6, $x – y = 2$

8.Find the value of $k$k for which the system has no solution:
$3x + ky = 2$, $6x + 2y = 5$

9.The sum of two numbers is 30 and their difference is 6. Find the numbers.

10. Solve the following pair of equations:

5x−2y=4, $3x + 2y = 16$

Answers sheet:

1. x=4, y=1
2. x=6, y=3
3. k=1
4. Inconsistent (No solution)
5. x=4, y=5
6. x=3, y=−1
7. $x = 4,\ y = 2$
8. k=1
9. Numbers are $18$ and $12$
10. x=2, y=3

These questions are repeated patterns from previous year papers, so practicing them will directly help in scoring better in board exams.

Conclusion

The chapter Pair of Linear Equations in Two Variables is very important for CBSE Class 10 Maths. By understanding the concepts and practicing different types of questions, students can easily score good marks in exams.

Regular practice of methods like substitution and elimination, along with solving previous year questions, will help in building strong confidence and accuracy. dont forget to join our telegram channel fir free. check other chapters below.

Thanks.