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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 MCQs on graphical method, elimination, substitution, cross multiplication, consistency, and word problems 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 focuses on solving two linear equations simultaneously using algebraic and graphical methods. Students learn to identify whether a system has one solution, no solution, or infinitely many solutions. These concepts are frequently tested in CBSE and State Board examinations and also help in solving practical mathematical problems.
What You Will Learn?
✔ Standard Form of Linear Equations
✔ Graphical Method
✔ Substitution Method
✔ Elimination Method
✔ Cross Multiplication Method
✔ Conditions for Consistency
✔ Real-Life Applications
✔ Board Exam Based Questions
Why This Topic Is Important?
Understanding pair of linear equations strengthens algebraic skills and logical reasoning. This chapter is the foundation for higher mathematics and is one of the most important scoring chapters in Class 10 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
$$3x+y=11$$
$$x-y=1$$
is:
A)
$$(3,2)$$
B)
$$(2,5)$$
C)
$$(4,-1)$$
D)
$$(5,-4)$$
Answer:
$$(3,2)$$
Useful Formula for this Question:
Add the equations to eliminate one variable.
Solution:
Given,
$$3x+y=11$$
$$x-y=1$$
Adding,
$$4x=12$$
$$x=3$$
Substitute into
$$x-y=1$$
$$3-y=1$$
$$y=2$$
Hence, the correct answer is:
$$(3,2)$$
Q2. Which method involves expressing one variable in terms of the other before solving?
A) Elimination Method
B) Graphical Method
C) Substitution Method
D) Cross Multiplication Method
Answer:
Substitution Method
Useful Formula for this Question:
Express one variable as
$$x=f(y)$$
or
$$y=f(x)$$
and substitute it into the second equation.
Solution:
The substitution method first isolates one variable and then substitutes its value into the second equation to obtain the solution.
Hence, the correct answer is:
Substitution Method
Q3. If
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
then the graphs of the equations are:
A) Parallel
B) Coincident
C) Intersecting
D) Perpendicular
Answer:
Intersecting
Useful Formula for this Question:
For a unique solution,
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
Solution:
When the ratios of the coefficients of
$$x$$
and
$$y$$
are unequal, the two lines intersect at one point.
Therefore, the equations have one unique solution.
Hence, the correct answer is:
Intersecting
Q4. If
$$2x+3y=19$$
and
$$x=5$$
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,
$$2x+3y=19$$
Substitute
$$x=5$$
$$2(5)+3y=19$$
$$10+3y=19$$
$$3y=9$$
$$y=3$$
Hence, the correct answer is:
$$3$$
Q5. A pair of equations having no common solution represents:
A) Coincident Lines
B) Intersecting Lines
C) Parallel Lines
D) Perpendicular Lines
Answer:
Parallel Lines
Useful Formula for this Question:
If
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
then the equations are parallel.
Solution:
Parallel lines never intersect.
Therefore, there is no common solution.
Hence, the correct answer is:
Parallel Lines
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 a unique solution?
Answer:
A unique solution is the single point that satisfies both linear equations. It occurs when the two lines intersect.
Q. Why is the substitution method useful?
Answer:
It is useful when one variable can be easily expressed in terms of the other, making calculations simpler.
Q. What do parallel lines indicate?
Answer:
Parallel lines indicate that the pair of linear equations has no solution because they never intersect.
Common Mistakes Students Make
❌ Forgetting to isolate a variable correctly in the substitution method.
❌ Using incorrect signs while adding or subtracting equations.
❌ Confusing intersecting lines with coincident lines.
❌ Applying the wrong consistency condition.
❌ Not checking the final answer in both equations.
Quick Revision Notes
✔ Intersecting lines have one unique solution.
✔ Parallel lines have no solution.
✔ Coincident lines have infinitely many solutions.
✔ The substitution method is useful when one variable is easy to isolate.
✔ Always verify the obtained values in both equations.
✔ Learn the consistency conditions for quick board exam revision.
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions – contain fresh, non-repeated, NCERT-based questions prepared for effective board exam practice. Solving these MCQs regularly improves conceptual understanding, calculation speed, and confidence, helping students achieve better scores in CBSE board exams, state board exams, school examinations, and scholarship tests.
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