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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs based on NCERT with method selection, error analysis, competency-based questions, detailed solutions, board exam insights, shortcut tricks, and latest CBSE pattern.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Competency-Based MCQs
Difficulty Level: Board Exam (Medium to Advanced)
Topic Covered:
✔ Method Selection
✔ Error Analysis
✔ Logical Reasoning
✔ Concept Application
Based On:
NCERT Latest Syllabus
Introduction:
Solving a pair of linear equations is not only about obtaining the correct answer but also about choosing the most efficient method and identifying common mistakes. In board examinations, students often lose marks because of sign errors, incorrect elimination, or choosing a lengthy method when a simpler one is available.
This practice set focuses on mathematical thinking rather than lengthy calculations. Students will learn how to identify the best solving method, recognize incorrect mathematical steps, and avoid common examination mistakes.
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Q1.
Which method is most suitable for solving the pair of equations?
$$x=5-y$$
$$2x+3y=11$$
Question Difficulty:
🟢 Easy
A) Graphical Method
B) Elimination Method
C) Substitution Method
D) Cross Multiplication Method
Answer:
$$\text{Substitution Method}$$
Useful Formula for this Question:
One variable is already isolated.
Concept Behind This Question:
Choose the method requiring minimum calculations.
Solution:
Since
$$x$$
is already expressed in terms of
$$y$$
the substitution method requires the fewest steps.
Therefore,
$$\text{Substitution Method}$$
is the correct answer.
Shortcut / Smart Trick
Whenever you see
$$x=\cdots$$
or
$$y=\cdots$$
think substitution first.
Board Exam Insight
Method-selection questions are becoming common in competency-based papers.
Teacher’s Smart Trick
Never start calculations before checking whether a variable is already isolated.
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Q2.
A student adds the equations
$$3x+y=8$$
$$3x-y=4$$
to eliminate
$$x$$
The student’s first step is:
Question Difficulty:
🟡 Medium
A) Correct
B) Incorrect because addition eliminates $$y$$
C) Incorrect because subtraction should be used
D) Cannot be determined
Answer:
$$\text{Incorrect because addition eliminates }y$$
Useful Formula for this Question:
Opposite coefficients disappear on addition.
Concept Behind This Question:
Understand which variable gets eliminated.
Solution:
Adding,
$$(3x+y)+(3x-y)=8+4$$
gives
$$6x=12$$
The variable
$$y$$
is eliminated.
Hence,
the student’s statement is incorrect.
Therefore,
Option
$$\text{B}$$
is correct.
Shortcut / Smart Trick
Before adding or subtracting,
check which coefficients are opposite.
Board Exam Insight
Error-analysis questions are increasingly asked in board exams.
Teacher’s Smart Trick
Write one extra line before calculation.
It prevents careless mistakes.
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Q3.
Which statement is correct?
Question Difficulty:
🟡 Medium
A) Elimination is always faster.
B) Substitution is always faster.
C) The best method depends on the given equations.
D) Graphical method is always the fastest.
Answer:
$$\text{The best method depends on the given equations.}$$
Useful Formula for this Question:
There is no universally fastest method.
Concept Behind This Question:
Different equations require different approaches.
Solution:
Some equations are better suited for substitution,
while others are easier using elimination.
Therefore,
the correct answer is
$$\text{Option C}$$
Shortcut / Smart Trick
Spend
5 seconds
choosing the method.
You may save
30 seconds
during calculations.
Board Exam Insight
Efficiency is part of mathematical reasoning.
Teacher’s Smart Trick
Good students choose the method before solving.
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Q4.
If both equations become identical after simplification,
the pair of equations has:
Question Difficulty:
🟢 Easy
A) One Solution
B) No Solution
C) Infinitely Many Solutions
D) Exactly Two Solutions
Answer:
$$\text{Infinitely Many Solutions}$$
Useful Formula for this Question:
Identical equations represent the same line.
Concept Behind This Question:
Coincident lines overlap completely.
Solution:
If both equations are identical,
every point satisfying one equation also satisfies the other.
Hence,
there are
$$\text{Infinitely Many Solutions}$$
Shortcut / Smart Trick
Same equation = Same line.
Board Exam Insight
This is one of the highest-weightage concepts in Chapter 3.
Teacher’s Smart Trick
Always simplify equations before comparing ratios.
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Q5.
Which mistake is most common while solving by elimination?
Question Difficulty:
🟡 Medium
A) Forgetting variable names
B) Sign mistakes during addition or subtraction
C) Drawing the graph
D) Writing the chapter name
Answer:
$$\text{Sign mistakes during addition or subtraction}$$
Useful Formula for this Question:
Careful sign handling is essential.
Concept Behind This Question:
Most calculation errors occur because of incorrect signs.
Solution:
Students generally understand the method correctly,
but they often make mistakes while adding or subtracting negative numbers.
Hence,
the correct answer is
$$\text{Sign mistakes during addition or subtraction}$$
Shortcut / Smart Trick
Circle every negative sign before calculating.
Board Exam Insight
Most wrong answers in elimination arise because of sign errors.
Teacher’s Smart Trick
Never perform mental subtraction when negative numbers are involved.
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Important Formulas and Concepts
✔ Substitution:
Use when one variable is already isolated.
✔ Elimination:
Use when coefficients can easily be made equal.
✔ Graphical Method:
Used for visual understanding.
✔ Cross Multiplication:
Useful when specifically asked.
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30-Second Revision Box
✅ Isolated variable → Substitution
✅ Equal coefficients → Elimination
✅ Same equations → Infinite solutions
✅ Parallel lines → No solution
✅ Intersecting lines → One solution
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Most Common Exam Mistake
Students often choose the correct method but lose marks because of incorrect addition or subtraction of signed numbers.
————————————————–
Expected Board Question
Which algebraic method would you prefer to solve a given pair of linear equations? Justify your answer.
————————————————–
Quick Revision Notes
✔ Read the equations carefully.
✔ Choose the easiest method.
✔ Check signs before calculations.
✔ Verify the ordered pair.
✔ Compare ratios whenever required.
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Conclusion:
This practice set helps students develop mathematical reasoning, identify common mistakes, and select the most efficient method for solving pair of linear equations. These skills are essential for success in the latest CBSE Board examinations.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-10
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-9
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-8
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-7
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-6
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-5
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-4
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two variables part-3
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-2
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Part 1
- Class 10 Maths Chapter 2 Polynomials (Graphical Zeroes) – Part 13
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
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