Chapter 3 · Class 10 CBSE · Free Worksheet PDF

Pair of Linear Equations in Two Variables Sums for Class 10 — Free CBSE Worksheet PDF with Answers

Download a free printable pair of linear equations in two variables worksheet for Class 10 CBSE with 30 practice questions covering pair of linear equations in two variables concepts, practice problems, and word problems with step-by-step solutions. Includes complete answer key. CBSE-aligned for the 2025-26 syllabus.

Last updated: 5 May 2026

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30 questions (Easy + Medium + Hard) with answer key. Fresh set generated daily.

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Sample Pair of Linear Equations in Two Variables Sums for Class 10 — Practice Questions

Here are 8 sample pair of linear equations in two variables sums from this Class 10 CBSE worksheet. Download the full PDF for all 30 questions with answers.

Q1.For a pair of linear equations in two variables, (x, y) = (p, q) is a solution if:
A.It satisfies the first equation only.
B.It satisfies the second equation only.
C.It satisfies both equations simultaneously.
D.It is a point on the x-axis.

Difficulty: Easy

Q2.If the graph of a pair of linear equations in two variables shows two lines intersecting at a single point, then the system of equations has:
A.No solution.
B.Exactly one solution.
C.Infinitely many solutions.
D.Two solutions.

Difficulty: Easy

Q3.For what value of 'k' will the pair of linear equations x + ky = 3 and 3x + 2y = 1 NOT have a unique solution?
A.2/3
B.1/3
C.-2/3
D.-1/3

Difficulty: Easy

Q4.Ravi is trying to solve the system: x + y = 7 and 2x - 3y = 4 using the substitution method. He correctly expresses x from the first equation as x = 7 - y. Which of the following is the correct next step to substitute into the second equation?
A.2(7 - y) - 3y = 4
B.7 - y - 3y = 4
C.2x - 3(7 - y) = 4
D.2(7 - y) - 3(7 - y) = 4

Difficulty: Easy

Q5.If x and y are two numbers such that their sum is 8 and twice the first number minus the second number is 7, which pair of linear equations represents this?
A.x + y = 7, 2x - y = 8
B.x + y = 8, x - 2y = 7
C.x + y = 8, 2x + y = 7
D.x + y = 8, 2x - y = 7

Difficulty: Easy

Q6.A pair of equations is called 'linear' because their graphical representation always forms:
A.Curves.
B.Circles.
C.Straight lines.
D.Paraboloids.

Difficulty: Easy

Q7.Which of the following pairs of equations represents parallel lines (no solution)?
A.x + 2y = 4, 2x + 4y = 8
B.x + 2y = 4, 2x - 4y = 6
C.x + 2y = 4, 3x + 6y = 10
D.x + 2y = 4, 4x + 8y = 16

Difficulty: Easy

Q8.If the graphs of two linear equations are the same line, how many solutions does the system have?
A.No solution.
B.Exactly one solution.
C.Infinitely many solutions.
D.Two solutions.

Difficulty: Easy

Answer Key — Sample Questions+
Q1:It satisfies both equations simultaneously.
Q2:Exactly one solution.
Q3:2/3
Q4:2(7 - y) - 3y = 4
Q5:x + y = 8, 2x - y = 7
Q6:Straight lines.
Q7:x + 2y = 4, 3x + 6y = 10
Q8:Infinitely many solutions.

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicPair of Linear Equations in Two Variables
BoardCBSE
Class10
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download free pair of linear equations in two variables sums for Class 10?+
You can download a free Pair of Linear Equations in Two Variables PDF worksheet for Class 10 CBSE right here on SparkEd. The worksheet includes 30 practice questions (pair of linear equations in two variables concepts, practice problems, and word problems with step-by-step solutions) at easy, medium, and hard levels with a complete answer key.
How many pair of linear equations in two variables questions are in this Class 10 worksheet?+
This SparkEd worksheet for Pair of Linear Equations in Two Variables Class 10 contains 30 questions — 10 easy, 10 medium, and 10 hard. The questions cover pair of linear equations in two variables concepts, practice problems, and word problems with step-by-step solutions. A fresh set is generated daily so students never repeat the same sheet.
Does the Pair of Linear Equations in Two Variables worksheet for Class 10 include answers?+
Yes! Every SparkEd worksheet comes with a complete answer key. Students can self-check their work after completing the sheet. The PDF is free to download and print.
Is this pair of linear equations in two variables worksheet aligned to CBSE syllabus?+
Yes. This worksheet is specifically designed for Class 10 CBSE students and aligned to the 2025-26 CBSE syllabus. All questions follow the CBSE exam pattern and difficulty level.
Can I print this Pair of Linear Equations in Two Variables worksheet?+
Absolutely! The worksheet downloads as an A4-size PDF that is ready to print. It includes the questions, space for working, and a separate answer key — perfect for classroom use or home practice.
How is this worksheet different from NCERT textbook exercises?+
SparkEd worksheets go beyond NCERT exercises by providing 30 questions at 3 progressive difficulty levels. Level 1 (Easy) builds confidence, Level 2 (Medium) tests application, and Level 3 (Hard) prepares for exams. Each worksheet includes word problems and conceptual questions, not just computation.
Does this worksheet include pair of linear equations in two variables word problems?+
Yes! The worksheet includes both computation-based questions and real-world word problems. Word problems are especially important for CBSE exams, and our worksheet covers a variety of scenarios to build problem-solving skills.

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