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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 unique NCERT-based MCQs on substitution, elimination, graphical method, consistency of equations, and applications with detailed solutions for CBSE and state board exams.
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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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
The chapter Pair of Linear Equations in Two Variables enables students to solve two unknown variables using systematic mathematical methods. It explains how equations can have one solution, no solution, or infinitely many solutions depending on the relationship between their coefficients. Regular practice of MCQs helps improve speed, conceptual clarity, and confidence for board examinations.
What You Will Learn?
✔ Solving Linear Equations
✔ Substitution Method
✔ Elimination Method
✔ Cross Multiplication Method
✔ Consistency of Equations
✔ Graphical Interpretation
✔ Word Problems Based on Linear Equations
✔ Board Exam Oriented Concepts
Why This Topic Is Important?
This chapter is one of the highest-scoring chapters in Class 10 Mathematics. Students learn techniques that are frequently used in Algebra and Coordinate Geometry. The concepts also develop logical thinking and analytical skills required in higher mathematics.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. The solution of the pair of equations
$$x+y=9$$
$$x-y=3$$
is:
A)
$$(5,4)$$
B)
$$(6,3)$$
C)
$$(4,5)$$
D)
$$(3,6)$$
Answer:
$$(6,3)$$
Useful Formula for this Question:
Add both equations to eliminate one variable.
Solution:
Given,
$$x+y=9$$
$$x-y=3$$
Adding,
$$2x=12$$
$$x=6$$
Substitute in the first equation,
$$6+y=9$$
$$y=3$$
Hence, the correct answer is:
$$(6,3)$$
Q2. Which method is generally most suitable when one equation already has one variable isolated?
A) Graphical Method
B) Prime Factorization
C) Substitution Method
D) Cross Multiplication Only
Answer:
Substitution Method
Useful Formula for this Question:
If one equation is in the form
$$x=f(y)$$
or
$$y=f(x)$$
then substitution is convenient.
Solution:
When one variable is already expressed in terms of the other, substituting its value into the second equation makes solving easy.
Hence, the correct answer is:
Substitution Method
Q3. The pair of equations
$$2x+5y=8$$
and
$$4x+10y=16$$
has:
A) One Solution
B) No Solution
C) Infinitely Many Solutions
D) Two Solutions
Answer:
Infinitely Many Solutions
Useful Formula for this Question:
If
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
then infinitely many solutions exist.
Solution:
Here,
$$\frac{2}{4}=\frac{5}{10}=\frac{8}{16}
=\frac12$$
All ratios are equal.
Therefore, both equations represent the same line.
Hence, the correct answer is:
Infinitely Many Solutions
Q4. The graphs of two inconsistent linear equations are:
A) Intersecting Lines
B) Coincident Lines
C) Parallel Lines
D) Perpendicular Lines
Answer:
Parallel Lines
Useful Formula for this Question:
For inconsistent equations,
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Solution:
Parallel lines never meet.
Therefore, they have no common solution.
Hence, the pair of equations is inconsistent.
Therefore, the correct answer is:
Parallel Lines
Q5. If
$$3x+y=11$$
and
$$x=2$$
then the value of
$$y$$
is:
A)
$$3$$
B)
$$4$$
C)
$$5$$
D)
$$6$$
Answer:
$$5$$
Useful Formula for this Question:
Substitute the known value into the equation.
Solution:
Given,
$$3x+y=11$$
Substitute
$$x=2$$
$$3(2)+y=11$$
$$6+y=11$$
$$y=5$$
Hence, the correct answer is:
$$5$$
Important Formulas and Concepts
Standard Form
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Unique Solution
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
No Solution
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Infinitely Many Solutions
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
Methods of Solving
✔ Graphical Method
✔ Substitution Method
✔ Elimination Method
✔ Cross Multiplication Method
FAQs
Q. Which method is best when one variable is already isolated?
Answer:
The substitution method is the most convenient because the value of one variable can be directly substituted into the second equation.
Q. What do parallel lines indicate?
Answer:
Parallel lines indicate that the pair of linear equations has no solution and is inconsistent.
Q. What do coincident lines represent?
Answer:
Coincident lines represent infinitely many solutions because both equations describe the same straight line.
Common Mistakes Students Make
❌ Forgetting to change signs while eliminating variables.
❌ Writing incorrect ratios while checking consistency.
❌ Substituting the wrong value into the second equation.
❌ Confusing coincident lines with intersecting lines.
❌ Making arithmetic mistakes during addition or subtraction.
Quick Revision Notes
✔ Add or subtract equations in the elimination method.
✔ Use substitution when one variable is already isolated.
✔ Intersecting lines give one unique solution.
✔ Parallel lines give no solution.
✔ Coincident lines give infinitely many solutions.
✔ Check consistency using:
$$\frac{a_1}{a_2},;
\frac{b_1}{b_2},;
\frac{c_1}{c_2}$$
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide unique NCERT-based practice for mastering substitution, elimination, graphical interpretation, and consistency of linear equations. Regular practice of such MCQs enhances conceptual understanding, improves problem-solving speed, and helps students score better in CBSE board exams, state board exams, school tests, and scholarship examinations.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-11
- 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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