अध्याय 3 · Class 10 UP Board · Free Worksheet PDF

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

Download a free printable pair of linear equations in two variables worksheet for Class 10 UP Board 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. UP Board-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 UP Board worksheet. Download the full PDF for all 30 questions with answers.

Q1.दो चरों x और y में एक रैखिक समीकरण का मानक रूप क्या है?
A.ax+by+c=0ax + by + c = 0
B.ax2+by+c=0ax^2 + by + c = 0
C.ax+by=c2ax + by = c^2
D.a/x+b/y+c=0a/x + b/y + c = 0

Difficulty: Easy

Q2.यदि दो रैखिक समीकरणों का आलेखीय निरूपण प्रतिच्छेदी रेखाएँ हैं, तो हल की संख्या क्या होगी?
A.एक अद्वितीय हल
B.कोई हल नहीं
C.अपरिमित रूप से अनेक हल
D.दो हल

Difficulty: Easy

Q3.दो रैखिक समीकरणों a1x+b1y+c1=0a_1x + b_1y + c_1 = 0 और a2x+b2y+c2=0a_2x + b_2y + c_2 = 0 के युग्म के अद्वितीय हल होने की शर्त क्या है?
A.a1/a2=b1/b2≠c1/c2a_1/a_2 = b_1/b_2 \neq c_1/c_2
B.a1/a2=b1/b2=c1/c2a_1/a_2 = b_1/b_2 = c_1/c_2
C.a1/a2≠b1/b2a_1/a_2 \neq b_1/b_2
D.a1/a2≠b1/b2=c1/c2a_1/a_2 \neq b_1/b_2 = c_1/c_2

Difficulty: Easy

Q4.यदि दो रैखिक समीकरणों का युग्म असंगत है, तो निम्न में से कौन सी शर्त सत्य है?
A.a1/a2=b1/b2≠c1/c2a_1/a_2 = b_1/b_2 \neq c_1/c_2
B.a1/a2=b1/b2=c1/c2a_1/a_2 = b_1/b_2 = c_1/c_2
C.a1/a2≠b1/b2a_1/a_2 \neq b_1/b_2
D.a1/a2=b1/b2a_1/a_2 = b_1/b_2

Difficulty: Easy

Q5.निम्न में से कौन सा समीकरण युग्म संगत है?
A.A) x+y=5x + y = 5, 2x+2y=112x + 2y = 11
B.B) x+2y=4x + 2y = 4, 2x+4y=122x + 4y = 12
C.C) x−y=8x - y = 8, 3x−3y=163x - 3y = 16
D.D) x+2y=3x + 2y = 3, 4x+3y=24x + 3y = 2

Difficulty: Easy

Q6.प्रतिस्थापन विधि में, दो चरों वाले रैखिक समीकरणों के युग्म को हल करने के लिए पहला चरण क्या होता है?
A.एक समीकरण से एक चर का मान दूसरे चर के पदों में व्यक्त करना।
B.दोनों समीकरणों को जोड़ना।
C.दोनों समीकरणों को गुणा करना।
D.आलेख बनाना।

Difficulty: Easy

Q7.दो संख्याओं का योग 35 है और उनका अंतर 13 है। यदि संख्याएँ x और y हैं, तो समीकरण युग्म क्या होगा?
A.A) x+y=35x + y = 35, x−y=13x - y = 13
B.B) x+y=13x + y = 13, x−y=35x - y = 35
C.C) xy=35xy = 35, x/y=13x/y = 13
D.D) x−y=35x - y = 35, x+y=13x + y = 13

Difficulty: Easy

Q8.निम्नलिखित में से कौन सा समीकरण दो चरों में एक रैखिक समीकरण का उदाहरण है?
A.x2+2y=5x^2 + 2y = 5
B.3x+4y=73x + 4y = 7
C.xy+y=9xy + y = 9
D.x+y=10\sqrt{x} + y = 10

Difficulty: Easy

Answer Key — Sample Questions+
Q1:$ax + by + c = 0$
Q2:एक अद्वितीय हल
Q3:$a_1/a_2 \neq b_1/b_2$
Q4:$a_1/a_2 = b_1/b_2 \neq c_1/c_2$
Q5:D) $x + 2y = 3$, $4x + 3y = 2$
Q6:एक समीकरण से एक चर का मान दूसरे चर के पदों में व्यक्त करना।
Q7:A) $x + y = 35$, $x - y = 13$
Q8:$3x + 4y = 7$

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

About This Worksheet

TopicPair of Linear Equations in Two Variables
BoardUP Board
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 UP Board 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 UP Board syllabus?+
Yes. This worksheet is specifically designed for Class 10 UP Board students and aligned to the 2025-26 UP Board syllabus. All questions follow the UP Board 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 UP Board exams, and our worksheet covers a variety of scenarios to build problem-solving skills.

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