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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. Solve intermediate-level questions using the elimination method with detailed solutions, shortcut tricks, board exam insights, and exam tips.
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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: Intermediate (Board Level)
Method Covered: Elimination Method
Based On: NCERT Latest Syllabus
Introduction:
In many pairs of linear equations, the coefficients of the variables are not equal. In such cases, we first multiply one or both equations by suitable numbers to make the coefficients of one variable equal. After that, we add or subtract the equations to eliminate one variable.
This approach is called the elimination method. It is one of the most reliable and efficient algebraic methods and is widely used in CBSE Board examinations. Students should practice these questions carefully because they improve calculation accuracy and logical thinking.
This practice set focuses on intermediate-level problems where multiplication is required before elimination.
What You Will Learn?
✔ Making Coefficients Equal
✔ Eliminating Variables
✔ Solving Intermediate Problems
✔ Verification of Solutions
✔ Shortcut Techniques
✔ Board Exam Preparation
Why This Topic Is Important?
Many board examination questions require students to multiply equations before applying the elimination method.
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. Solve:
$$2x+y=7$$
$$x-y=2$$
A) $$(3,\ 1)$$
B) $$(2,\ 3)$$
C) $$(1,\ 5)$$
D) $$(4,\ -1)$$
Answer:
$$(3,\ 1)$$
Useful Formula for this Question:
Eliminate $$y$$ by adding the equations.
Concept Behind This Question:
The coefficients of $$y$$ are already opposite.
Solution:
Adding both equations:
$$(2x+y)+(x-y)=7+2$$
$$3x=9$$
$$x=3$$
Substitute into:
$$x-y=2$$
$$3-y=2$$
$$y=1$$
Therefore, the solution is:
$$(3,\ 1)$$
Shortcut / Smart Trick
Always check whether a variable is already ready for elimination before multiplying the equations.
Board Exam Insight
Direct elimination questions like this are common in 1-mark MCQs.
Exam Tip:
Look for opposite coefficients before performing any multiplication.
————————————————–
Q2. Solve:
$$2x+y=8$$
$$3x-y=7$$
A) $$(3,\ 2)$$
B) $$(2,\ 4)$$
C) $$(1,\ 6)$$
D) $$(4,\ 0)$$
Answer:
$$(3,\ 2)$$
Useful Formula for this Question:
Add the equations to eliminate $$y$$.
Concept Behind This Question:
Opposite coefficients simplify elimination.
Solution:
Adding both equations:
$$5x=15$$
$$x=3$$
Substitute into:
$$2x+y=8$$
$$6+y=8$$
$$y=2$$
Therefore, the solution is:
$$(3,\ 2)$$
Shortcut / Smart Trick
After elimination, substitute into the equation with smaller coefficients.
Board Exam Insight
Always verify the ordered pair before marking the answer.
Exam Tip:
Simple substitution prevents calculation mistakes.
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Q3. Solve:
$$2x+y=5$$
$$x+2y=4$$
A) $$(2,\ 1)$$
B) $$(1,\ 2)$$
C) $$(3,\ -1)$$
D) $$(0,\ 2)$$
Answer:
$$(2,\ 1)$$
Useful Formula for this Question:
Multiply one equation to make coefficients equal.
Concept Behind This Question:
Equal coefficients allow elimination.
Solution:
Multiply the second equation by:
$$2$$
$$2x+4y=8$$
Subtract the first equation:
$$(2x+4y)-(2x+y)=8-5$$
$$3y=3$$
$$y=1$$
Substitute into:
$$2x+y=5$$
$$2x+1=5$$
$$2x=4$$
$$x=2$$
Therefore, the solution is:
$$(2,\ 1)$$
Shortcut / Smart Trick
Choose the multiplication that produces the smallest coefficients.
Board Exam Insight
Questions requiring multiplication before elimination frequently appear in competency-based papers.
Exam Tip:
Write each multiplied equation clearly to avoid sign errors.
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Q4. Solve:
$$3x+y=13$$
$$x+y=7$$
A) $$(3,\ 4)$$
B) $$(2,\ 5)$$
C) $$(4,\ 1)$$
D) $$(5,\ 2)$$
Answer:
$$(3,\ 4)$$
Useful Formula for this Question:
Subtract the equations to eliminate $$y$$.
Concept Behind This Question:
Equal coefficients with the same sign require subtraction.
Solution:
Subtract the second equation from the first:
$$(3x+y)-(x+y)=13-7$$
$$2x=6$$
$$x=3$$
Substitute into:
$$x+y=7$$
$$3+y=7$$
$$y=4$$
Therefore, the solution is:
$$(3,\ 4)$$
Shortcut / Smart Trick
Same coefficients and same signs → subtract directly.
Board Exam Insight
Recognizing when subtraction is needed saves time.
Exam Tip:
Never add equations with equal coefficients having the same sign.
————————————————–
Q5. Solve:
$$4x+y=17$$
$$2x-y=1$$
A) $$(3,\ 5)$$
B) $$(2,\ 9)$$
C) $$(4,\ 1)$$
D) $$(5,\ -3)$$
Answer:
$$(3,\ 5)$$
Useful Formula for this Question:
Add the equations to eliminate $$y$$.
Concept Behind This Question:
Opposite coefficients simplify calculations.
Solution:
Adding the equations:
$$6x=18$$
$$x=3$$
Substitute into:
$$4x+y=17$$
$$12+y=17$$
$$y=5$$
Therefore, the solution is:
$$(3,\ 5)$$
Shortcut / Smart Trick
Always substitute into the equation with the smaller coefficients if possible.
Board Exam Insight
Intermediate elimination questions are common in both objective and subjective sections.
Exam Tip:
Verify the final ordered pair in both equations before selecting the answer.
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Important Formulas and Concepts
Elimination Method
Step 1:
Make one variable’s coefficients equal.
Step 2:
Add or subtract the equations.
Step 3:
Find one variable.
Step 4:
Substitute into an original equation.
Step 5:
Write the solution as:
$$(x,\ y)$$
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FAQs
Q. Why do we multiply equations before elimination?
Answer:
To make the coefficients of one variable equal, allowing easy elimination.
Q. Which operation should be used after making coefficients equal?
Answer:
Use addition if the coefficients have opposite signs, and subtraction if they have the same sign.
Q. Is elimination faster than substitution?
Answer:
In many cases, yes. It depends on the given equations.
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Common Mistakes Students Make
❌ Multiplying only one side of an equation.
❌ Forgetting to multiply every term.
❌ Sign mistakes during subtraction.
❌ Not substituting back correctly.
❌ Writing only one variable instead of the ordered pair.
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Quick Revision Notes
✔ Make coefficients equal.
✔ Same signs → Subtract.
✔ Opposite signs → Add.
✔ Find one variable.
✔ Substitute back.
✔ Write the final answer as:
$$(x,\ y)$$
Related links
- 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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