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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers based on the latest NCERT syllabus. Learn the elimination method with step-by-step solutions, shortcut tricks, board exam insights, and detailed explanations.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Board Exam Level
Method Covered: Elimination Method (Basic)
Based On: NCERT Latest Syllabus
Introduction:
The elimination method is one of the most important algebraic methods used to solve a pair of linear equations in two variables. In this method, one variable is eliminated by making its coefficients equal in both equations. The resulting equation contains only one variable, making it easier to solve.
This method is especially useful when the coefficients of one variable are already equal or can easily be made equal by multiplying the equations with suitable numbers. Because of its systematic approach, the elimination method is widely used in NCERT textbooks and CBSE Board examinations.
In this practice set, students will learn the basic concepts of elimination and solve simple numerical problems using step-by-step explanations.
What You Will Learn?
✔ Meaning of Elimination Method
✔ Eliminating One Variable
✔ Solving Linear Equations
✔ Finding Ordered Pairs
✔ Verification of Solutions
✔ Board Exam Concepts
Why This Topic Is Important?
The elimination method is one of the fastest algebraic methods and is frequently used in board examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
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Q1. In the elimination method, the first objective is to:
Question Difficulty:
🟢 Easy
A) Draw the graph
B) Eliminate one variable
C) Find the midpoint
D) Calculate the slope
Answer:
$$\text{Eliminate one variable}$$
Useful Formula for this Question:
Multiply the equations (if necessary) so that the coefficients of one variable become equal.
Concept Behind This Question:
After eliminating one variable, only one unknown remains.
Solution:
The elimination method reduces two equations to one equation by removing one variable.
Therefore, the correct answer is:
$$\text{Eliminate one variable}$$
Shortcut / Smart Trick
Choose the variable whose coefficients are already equal or can easily be made equal.
Board Exam Insight
This concept is frequently asked in 1-mark conceptual MCQs.
Exam Tip:
Always check whether addition or subtraction will eliminate the chosen variable.
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Q2. Solve:
$$x+y=9$$
$$x-y=3$$
Question Difficulty:
🟢 Easy
A) $$(5,\ 4)$$
B) $$(6,\ 3)$$
C) $$(4,\ 5)$$
D) $$(3,\ 6)$$
Answer:
$$(6,\ 3)$$
Useful Formula for this Question:
Add the equations to eliminate $$y$$.
Concept Behind This Question:
The coefficients of $$y$$ are already opposite.
Solution:
Adding both equations:
$$(x+y)+(x-y)=9+3$$
$$2x=12$$
$$x=6$$
Substitute into:
$$x+y=9$$
$$6+y=9$$
$$y=3$$
Therefore, the solution is:
$$(6,\ 3)$$
Shortcut / Smart Trick
If one equation has $$+y$$ and the other has $$-y$$, simply add them.
Board Exam Insight
Such questions are among the easiest scoring questions in the objective section.
Exam Tip:
After finding $$x$$, substitute into the simpler equation.
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Q3. Solve:
$$2x+y=11$$
$$2x-y=5$$
Question Difficulty:
🟢 Easy
A) $$(4,\ 3)$$
B) $$(3,\ 5)$$
C) $$(5,\ 1)$$
D) $$(2,\ 7)$$
Answer:
$$(4,\ 3)$$
Useful Formula for this Question:
Add the equations to eliminate $$y$$.
Concept Behind This Question:
The coefficients of $$y$$ are additive inverses.
Solution:
Adding the equations:
$$4x=16$$
$$x=4$$
Substitute into:
$$2x+y=11$$
$$8+y=11$$
$$y=3$$
Therefore, the correct answer is:
$$(4,\ 3)$$
Shortcut / Smart Trick
When the coefficients are already opposite, never multiply the equations unnecessarily.
Board Exam Insight
Direct elimination questions appear regularly in CBSE sample papers.
Exam Tip:
Look for opposite signs before starting calculations.
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Q4. In the elimination method, if the coefficients of a variable are equal and have the same sign, we should:
Question Difficulty:
🟡 Medium
A) Add the equations
B) Subtract one equation from the other
C) Draw the graph
D) Divide both equations
Answer:
$$\text{Subtract one equation from the other}$$
Useful Formula for this Question:
Equal coefficients with the same sign are eliminated by subtraction.
Concept Behind This Question:
Subtraction makes the coefficients cancel.
Solution:
If both coefficients are equal and have the same sign, subtraction eliminates that variable immediately.
Therefore, the correct answer is:
$$\text{Subtract one equation from the other}$$
Shortcut / Smart Trick
Same signs → Subtract
Opposite signs → Add
Board Exam Insight
This rule is often tested directly in MCQs.
Exam Tip:
Memorize the “Same Sign–Subtract, Opposite Sign–Add” rule.
————————————————–
Q5. Solve:
$$3x+y=10$$
$$3x-y=8$$
Question Difficulty:
🟡 Medium
A) $$(3,\ 1)$$
B) $$(2,\ 4)$$
C) $$(4,\ -2)$$
D) $$(1,\ 7)$$
Answer:
$$(3,\ 1)$$
Useful Formula for this Question:
Add the equations to eliminate $$y$$.
Concept Behind This Question:
Adding removes $$y$$ because the coefficients are opposite.
Solution:
Adding the equations:
$$6x=18$$
$$x=3$$
Substitute into:
$$3x+y=10$$
$$9+y=10$$
$$y=1$$
Therefore, the solution is:
$$(3,\ 1)$$
Shortcut / Smart Trick
Always choose the operation that eliminates a variable in one step.
Board Exam Insight
Students who identify the correct operation first solve these questions much faster.
Exam Tip:
Verify the ordered pair in both equations before marking the answer.
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Important Formulas and Concepts
Elimination Method
Step 1:
Make the coefficients of one variable equal.
Step 2:
Add or subtract the equations.
Step 3:
Find one variable.
Step 4:
Substitute into either equation.
Step 5:
Write the final answer as:
$$(x,\ y)$$
————————————————–
FAQs
Q. When is the elimination method most useful?
Answer:
When the coefficients of one variable are equal or can easily be made equal.
Q. How do we decide between addition and subtraction?
Answer:
Use addition for opposite signs and subtraction for the same signs.
Q. Should the final answer always be verified?
Answer:
Yes. Substitute the ordered pair into both original equations.
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Common Mistakes Students Make
❌ Adding instead of subtracting.
❌ Forgetting to multiply equations when required.
❌ Sign errors during elimination.
❌ Writing only one variable as the answer.
❌ Not checking the final solution.
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Quick Revision Notes
✔ Eliminate one variable first.
✔ Same signs → Subtract.
✔ Opposite signs → Add.
✔ Substitute back to find the second variable.
✔ Final answer should always be written as:
$$(x,\ y)$$
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Conclusion:
These Class 10 Maths Chapter 3 MCQs help students understand the elimination method through simple and systematic examples. Regular practice improves calculation speed, algebraic accuracy, and confidence for school and board examinations.
Related links
- 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 graphical representation of polynomials – Part 12
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials ) – Part 11
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
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