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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 to solve linear equations using the substitution 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: Substitution Method (Numerical Problems)
Based On: NCERT Latest Syllabus
Introduction:
After understanding the basic idea of the substitution method, students should practice solving actual numerical problems. In this method, one variable is expressed in terms of the other and then substituted into the second equation. This reduces the system of two equations to a single equation in one variable.
The substitution method is particularly useful when one equation is already solved for one variable or can easily be rearranged. It develops algebraic thinking, improves calculation speed, and is frequently tested in CBSE Board examinations.
This practice set focuses on solving equations completely using substitution. Every solution is explained step by step so that students understand the logic behind each calculation rather than simply memorizing the process.
What You Will Learn?
✔ Solving by Substitution
✔ Rearranging Equations
✔ Finding Both Variables
✔ Verification of Solutions
✔ Shortcut Techniques
✔ Board Exam Concepts
Why This Topic Is Important?
The substitution method is one of the three prescribed algebraic methods in NCERT and is widely used in school and 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. The solution of $$x+y=8$$ and $$x-y=2$$ is:
A) $$(5,\ 3)$$
B) $$(4,\ 4)$$
C) $$(6,\ 2)$$
D) $$(3,\ 5)$$
Answer:
$$(5,\ 3)$$
Useful Formula for this Question:
Substitution Method
Concept Behind This Question:
Find one variable first, then substitute back.
Solution:
From
$$x-y=2$$
we get
$$x=y+2$$
Substitute into
$$x+y=8$$
$$(y+2)+y=8$$
$$2y=6$$
$$y=3$$
Now,
$$x=3+2=5$$
Therefore, the solution is
$$(5,\ 3)$$
Shortcut / Smart Trick
Whenever one equation can be written as
$$x=\cdots$$
or
$$y=\cdots$$
the substitution method becomes very easy.
Board Exam Insight
Questions of this type are commonly asked as 1-mark MCQs and 2-mark short-answer questions.
Exam Tip:
Always verify the ordered pair in both equations.
————————————————–
Q2. Solve $$x+y=10$$ $$x-y=4$$ .
A) $$(7,\ 3)$$
B) $$(6,\ 4)$$
C) $$(8,\ 2)$$
D) $$(5,\ 5)$$
Answer:
$$(7,\ 3)$$
Useful Formula for this Question:
Substitution Method
Concept Behind This Question:
Express one variable in terms of the other.
Solution:
From
$$x-y=4$$
$$x=y+4$$
Substitute into
$$x+y=10$$
$$(y+4)+y=10$$
$$2y=6$$
$$y=3$$
Then
$$x=7$$
Therefore,
$$(7,\ 3)$$
is the correct solution.
Shortcut / Smart Trick
If the equations contain
$$+y$$
and
$$-y$$
you may mentally check the options quickly.
Board Exam Insight
Students often lose marks by forgetting to substitute back for the second variable.
Exam Tip:
Always calculate both variables before selecting an option.
————————————————–
Q3. Which ordered pair satisfies $$2x+y=9$$ and $$x=3$$ .
A) $$(3,\ 3)$$
B) $$(3,\ 2)$$
C) $$(2,\ 5)$$
D) $$(4,\ 1)$$
Answer:
$$(3,\ 3)$$
Useful Formula for this Question:
Substitute the known value directly.
Concept Behind This Question:
One variable is already known.
Solution:
Substitute
$$x=3$$
into
$$2x+y=9$$
$$2(3)+y=9$$
$$6+y=9$$
$$y=3$$
Therefore,
$$(3,\ 3)$$
is the correct answer.
Shortcut / Smart Trick
Whenever one variable is already given, directly substitute it without rearranging the equation.
Board Exam Insight
These direct substitution questions are common in objective sections.
Exam Tip:
Do not skip simple substitution questions; they are easy scoring opportunities.
————————————————–
Q4. Solve $$y=x+1$$ and $$x+y=7$$ .
A) $$(3,\ 4)$$
B) $$(4,\ 3)$$
C) $$(2,\ 5)$$
D) $$(5,\ 2)$$
Answer:
$$(3,\ 4)$$
Useful Formula for this Question:
Substitute the given expression into the second equation.
Concept Behind This Question:
The value of one variable is already expressed in terms of the other.
Solution:
Substitute
$$y=x+1$$
into
$$x+y=7$$
$$x+(x+1)=7$$
$$2x+1=7$$
$$2x=6$$
$$x=3$$
Then
$$y=4$$
Therefore,
$$(3,\ 4)$$
is the correct answer.
Shortcut / Smart Trick
Use the equation that is already solved for one variable.
Board Exam Insight
This pattern appears regularly in CBSE sample papers.
Exam Tip:
Check your final ordered pair in both equations.
————————————————–
Q5. The solution of $$x=2y$$ and $$x+y=9$$ is:
A) $$(6,\ 3)$$
B) $$(3,\ 6)$$
C) $$(4,\ 5)$$
D) $$(5,\ 4)$$
Answer:
$$(6,\ 3)$$
Useful Formula for this Question:
Replace the variable using substitution.
Concept Behind This Question:
One equation already gives the value of
$$x$$
in terms of
$$y$$.
Solution:
Substitute
$$x=2y$$
into
$$x+y=9$$
$$2y+y=9$$
$$3y=9$$
$$y=3$$
Now,
$$x=6$$
Therefore,
$$(6,\ 3)$$
is the correct answer.
Shortcut / Smart Trick
Whenever one variable is already expressed as a multiple of the other, substitution is usually the fastest method.
Board Exam Insight
Such numerical questions frequently appear in competency-based MCQs.
Exam Tip:
After finding one variable, always substitute back carefully.
————————————————–
Important Formulas and Concepts
Substitution Method
Step 1:
Express one variable in terms of the other.
Step 2:
Substitute into the second equation.
Step 3:
Solve for one variable.
Step 4:
Substitute back.
Step 5:
Write the final answer as
$$(x,\ y)$$
————————————————–
FAQs
Q. Which method is easiest when one variable is already isolated?
Answer:
The substitution method.
Q. Should the final answer always be verified?
Answer:
Yes. Substitute the values into both original equations.
Q. Can substitution be used for all linear equations?
Answer:
Yes, although another algebraic method may sometimes require fewer calculations.
————————————————–
Common Mistakes Students Make
❌ Rearranging equations incorrectly.
❌ Making sign errors during substitution.
❌ Forgetting to calculate the second variable.
❌ Writing only one variable as the final answer.
❌ Not verifying the solution.
————————————————–
Quick Revision Notes
✔ Express one variable first.
✔ Substitute into the second equation.
✔ Solve for one variable.
✔ Find the second variable.
✔ Verify both equations.
✔ Final answer should always be written as
$$(x,\ y)$$
————————————————–
Conclusion:
These Class 10 Maths Chapter 3 MCQs strengthen students’ understanding of solving a pair of linear equations using the substitution method. Regular practice improves algebraic skills, calculation accuracy, and confidence for board examinations.
Related links
- 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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