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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 board exam-oriented MCQs on graphical method, substitution, elimination, cross multiplication, consistency, and word problems with detailed solutions.
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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 explains how two linear equations can be solved simultaneously using different mathematical methods. Students learn graphical interpretation, algebraic techniques, and practical applications of linear equations in solving everyday problems involving age, money, distance, and mixtures. Regular MCQ practice improves conceptual understanding and board exam preparation.
What You Will Learn?
✔ Pair of Linear Equations
✔ Graphical Representation
✔ Substitution Method
✔ Elimination Method
✔ Cross Multiplication Method
✔ Consistency of Equations
✔ Word Problems
✔ Board Exam Concepts
Why This Topic Is Important?
This chapter is a fundamental part of Algebra and is frequently asked in CBSE and State Board examinations. A strong understanding of linear equations helps students solve many higher-level mathematical problems accurately.
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
$$2x+y=8$$
$$x-y=1$$
is:
A)
$$(2,4)$$
B)
$$(3,2)$$
C)
$$(4,0)$$
D)
$$(5,-2)$$
Answer:
$$(3,2)$$
Useful Formula for this Question:
Add the equations after making the coefficients suitable.
Solution:
Given,
$$2x+y=8$$
$$x-y=1$$
Adding,
$$3x=9$$
$$x=3$$
Substitute into
$$x-y=1$$
$$3-y=$$
$$y=2$$
Hence, the correct answer is:
$$(3,2)$$
Q2. Which algebraic method involves multiplying the equations before eliminating a variable?
A) Substitution Method
B) Elimination Method
C) Graphical Method
D) Trial Method
Answer:
Elimination Method
Useful Formula for this Question:
Multiply one or both equations so that the coefficients of one variable become equal.
Solution:
In the elimination method, equations are multiplied by suitable numbers to make the coefficients of one variable equal before adding or subtracting them.
Hence, the correct answer is:
Elimination Method
Q3. If
$$9x+4y=30$$
and
$$x=2$$
then the value of
$$y$$
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,
$$9x+4y=30$$
Substitute
$$x=2$$
$$18+4y=30$$
$$4y=12$$
$$y=3$$
Hence, the correct answer is:
$$3$$
Q4. If two equations have one and only one common solution, then their graphs are:
A) Coincident Lines
B) Parallel Lines
C) Intersecting Lines
D) Curved Lines
Answer:
Intersecting Lines
Useful Formula for this Question:
If
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
then the equations have one unique solution.
Solution:
Two intersecting straight lines meet at exactly one point.
That common point is the unique solution of the pair of equations.
Hence, the correct answer is:
Intersecting Lines
Q5. The sum of two numbers is 18 and their difference is 4. Which pair of equations correctly represents this situation?
A)
$$x+y=18,\quad x-y=4$$
B)
$$x+y=4,\quad x-y=18$$
C)
$$x-y=14,\quad x+y=22$$
D)
$$2x+y=18,\quad x-y=4$$
Answer:
$$x+y=18,\quad x-y=4$$
Useful Formula for this Question:
For number problems,
Sum = Addition
Difference = Subtraction
Solution:
If the two numbers are
$$x$$
and
$$y$$
then,
Sum:
$$x+y=18$$
Difference:
$$x-y=4$$
Hence, the correct answer is:
$$x+y=18,\quad x-y=4$$
Important Formulas and Concepts
Standard Form
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Condition for Unique Solution
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
Condition for No Solution
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Condition for 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 unique solution?
Answer:
A unique solution is the single ordered pair that satisfies both linear equations simultaneously.
Q. Which method is useful when coefficients can easily be made equal?
Answer:
The elimination method is the most suitable because one variable can be removed by addition or subtraction.
Q. How are linear equations used in daily life?
Answer:
Linear equations are used in solving problems related to age, money, distance, speed, mixtures, shopping, and business calculations.
Common Mistakes Students Make
❌ Forming incorrect equations from word problems.
❌ Forgetting to substitute the value back into the second equation.
❌ Making arithmetic mistakes while eliminating variables.
❌ Confusing parallel lines with coincident lines.
❌ Using incorrect consistency conditions.
Quick Revision Notes
✔ A pair of linear equations has two variables.
✔ Intersecting lines have one unique solution.
✔ Parallel lines have no solution.
✔ Coincident lines have infinitely many solutions.
✔ Elimination and substitution are the most commonly used algebraic methods.
✔ 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 – include fresh, unique, and NCERT-based questions designed for effective board exam preparation. Regular practice of these MCQs strengthens conceptual understanding, improves accuracy and speed, and helps students achieve better results in CBSE board exams, state board exams, school examinations, and scholarship tests.
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