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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 fresh, board exam-oriented MCQs on graphical method, elimination, substitution, cross multiplication, consistency, and real-life applications 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 helps students solve two unknown variables using algebraic and graphical methods. It also explains the conditions under which two equations have one solution, no solution, or infinitely many solutions. These concepts are important for CBSE and State Board examinations and are widely applied in solving real-life mathematical problems.
What You Will Learn?
✔ Standard Form of Linear Equations
✔ Graphical Method
✔ Elimination Method
✔ Substitution Method
✔ Cross Multiplication Method
✔ Consistency of Equations
✔ Applications in Daily Life
✔ Board Exam Concepts
Why This Topic Is Important?
This chapter forms the basis of Algebra and develops problem-solving skills. It is one of the most important and scoring chapters in Class 10 Mathematics because questions are regularly asked 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
Q1. The solution of the equations
$$x+y=11$$
$$2x-y=4$$
is:
A)
$$(5,6)$$
B)
$$(4,7)$$
C)
$$(6,5)$$
D)
$$(7,4)$$
Answer:
$$(5,6)$$
Useful Formula for this Question:
Add the equations to eliminate one variable.
Solution:
Given,
$$x+y=11$$
$$2x-y=4$$
Adding,
$$3x=15$$
$$x=5$$
Substitute into
$$x+y=11$$
$$5+y=11$$
$$y=6$$
Hence, the correct answer is:
$$(5,6)$$
Q2. Which method is generally preferred when the coefficients of one variable are already equal?
A) Graphical Method
B) Elimination Method
C) Prime Factorization Method
D) Cross Multiplication Method
Answer:
Elimination Method
Useful Formula for this Question:
If the coefficients of one variable are equal or can easily be made equal, eliminate that variable by adding or subtracting the equations.
Solution:
The elimination method becomes the simplest approach when the coefficients of one variable are already the same or opposites.
Hence, the correct answer is:
Elimination Method
Q3. If
$$6x+5y=39$$
and
$$x=4$$
then the value of
$$y$$
is:
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$3$$
Useful Formula for this Question:
Substitute the given value into the equation.
Solution:
Given,
$$6x+5y=39$$
Substitute
$$x=4$$
$$24+5y=39$$
$$5y=15$$
$$y=3$$
Hence, the correct answer is:
$$3$$
Q4. If
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
then the pair of equations has:
A) One Unique Solution
B) Infinitely Many Solutions
C) No Solution
D) Two Solutions
Answer:
No Solution
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:
The equations represent two parallel lines.
Since parallel lines never intersect, they have no common solution.
Hence, the correct answer is:
No Solution
Q5. The cost of one notebook is ₹40 and one pen is ₹10. If x represents the number of notebooks and y represents the number of pens, which equation represents a total cost of ₹180?
A)
$$40x+10y=180$$
B)
$$40x-10y=180$$
C)
$$10x+40y=180$$
D)
$$40xy=180$$
Answer:
$$40x+10y=180$$
Useful Formula for this Question:
Total Cost = (Price × Quantity) + (Price × Quantity)
Solution:
Cost of one notebook
$$=₹40$$
Cost of one pen
$$=₹10$$
Therefore,
$$40x+10y=180$$
represents the total cost.
Hence, the correct answer is:
$$40x+10y=180$$
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 easiest when coefficients are already equal?
Answer:
The elimination method is usually the easiest because one variable can be removed directly.
Q. What does an inconsistent pair of equations mean?
Answer:
An inconsistent pair has no common solution because the corresponding lines are parallel.
Q. Why are pair of linear equations important?
Answer:
They are useful in solving real-life problems related to age, shopping, distance, speed, business, and many other practical situations.
Common Mistakes Students Make
❌ Using subtraction instead of addition while forming equations from word problems.
❌ Ignoring the coefficient signs during elimination.
❌ Mixing up the conditions for parallel and coincident lines.
❌ Forgetting to verify the obtained solution.
❌ Making arithmetic mistakes during substitution.
Quick Revision Notes
✔ Every linear equation represents a straight line.
✔ Intersecting lines have one unique solution.
✔ Parallel lines have no solution.
✔ Coincident lines have infinitely many solutions.
✔ Elimination is useful when coefficients are equal.
✔ Always check the final answer in both equations.
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions –provide fresh, unique, and NCERT-based board exam practice without repeating previous questions. Regular practice of these MCQs improves conceptual understanding, calculation accuracy, and problem-solving speed, helping students perform confidently in CBSE board exams, state board exams, school tests, and scholarship examinations.
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