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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 graphical method, substitution, elimination, consistency, and real-life 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 helps students understand how two linear equations can be solved simultaneously to determine the values of two unknown variables. Students learn different algebraic and graphical methods to solve equations efficiently. The concepts learned in this chapter are useful not only in board examinations but also in solving many real-life mathematical problems.
What You Will Learn?
✔ Standard Form of Linear Equations
✔ Graphical Representation
✔ Elimination Method
✔ Substitution Method
✔ Cross Multiplication Method
✔ Consistency of Equations
✔ Daily Life Applications
✔ Board Exam Concepts
Why This Topic Is Important?
This chapter develops analytical thinking and problem-solving abilities. Questions based on linear equations frequently appear in board examinations, making this chapter one of the most scoring topics in Class 10 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 equations
$$x+y=10$$
$$2x-y=5$$
is:
A)
$$(5,5)$$
B)
$$(4,6)$$
C)
$$(3,7)$$
D)
$$(6,4)$$
Answer:
$$(5,5)$$
Useful Formula for this Question:
Add the equations to eliminate one variable.
Solution:
Given,
$$x+y=10$$
$$2x-y=5$$
Adding,
$$3x=15$$
$$x=5$$
Substitute into
$$x+y=10$$
$$5+y=10$$
$$y=5$$
Hence, the correct answer is:
$$(5,5)$$
Q2. If two lines intersect, the pair of equations is called:
A) Inconsistent
B) Dependent
C) Consistent
D) Parallel
Answer:
Consistent
Useful Formula for this Question:
If
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
then the equations are consistent and have one unique solution.
Solution:
Intersecting lines always have one common point.
Therefore, the pair of equations has one unique solution and is called consistent.
Hence, the correct answer is:
Consistent
Q3. Which of the following is not a method for solving a pair of linear equations?
A) Elimination Method
B) Substitution Method
C) Graphical Method
D) Prime Factorization Method
Answer:
Prime Factorization Method
Useful Formula for this Question:
The four standard methods are:
✔ Graphical
✔ Substitution
✔ Elimination
✔ Cross Multiplication
Solution:
Prime factorization is used for finding factors of numbers, not for solving linear equations.
Hence, the correct answer is:
Prime Factorization Method
Q4. If
$$4x+y=17$$
and
$$y=5$$
then the value of
$$x$$
is:
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$3$$
Useful Formula for this Question:
Substitute the known value into the equation.
Solution:
Given,
$$4x+y=17$$
Substitute
$$y=5$$
$$4x+5=17$$
$$4x=12$$
$$x=3$$
Hence, the correct answer is:
$$3$$
Q5. Which of the following represents two parallel lines?
A)
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
B)
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
C)
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
D) None of these
Answer:
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Useful Formula for this Question:
Parallel lines satisfy
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Solution:
Parallel lines never intersect.
Therefore, the pair of equations has no solution.
Hence, the correct answer is
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
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. What is meant by a consistent pair of linear equations?
Answer:
A consistent pair of linear equations has at least one solution. It may have one unique solution or infinitely many solutions.
Q. Why are parallel lines called inconsistent?
Answer:
Parallel lines never intersect, so they have no common solution. Therefore, they are called inconsistent.
Q. Which method is useful when one variable is already known?
Answer:
The substitution method is the most convenient because the known value can be directly substituted into the other equation.
Common Mistakes Students Make
❌ Using the wrong consistency condition.
❌ Forgetting to verify the obtained values in both equations.
❌ Making calculation mistakes during elimination.
❌ Confusing parallel and coincident lines.
❌ Ignoring negative signs during substitution.
Quick Revision Notes
✔ Intersecting lines have one unique solution.
✔ Parallel lines have no solution.
✔ Coincident lines have infinitely many solutions.
✔ Use substitution when one variable is easy to isolate.
✔ Elimination is useful when coefficients can be made equal.
✔ Always verify the final solution in both equations.
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions – contain fresh, NCERT-based, non-repeated questions designed for effective board exam preparation. Practising these MCQs will strengthen conceptual understanding, improve problem-solving accuracy, and help students perform confidently in CBSE board exams, state board exams, school tests, and scholarship examinations.
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