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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers based on NCERT syllabus. Learn graphical representation, intersecting lines, parallel lines, coincident lines, and types of solutions with detailed explanations and board exam tips.
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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: Board Exam Foundation Level
Based On: NCERT Latest Syllabus
Introduction:
Every linear equation in two variables represents a straight line on the Cartesian plane. When two linear equations are plotted together, three different situations may arise. The two lines may intersect at one point, remain parallel without meeting, or completely overlap each other.
The graphical method is one of the easiest ways to understand whether a pair of linear equations has one solution, no solution, or infinitely many solutions. Although board examinations often focus on algebraic methods, understanding graphs builds strong conceptual clarity and makes solving equations much easier.
In this practice set, students will learn the basic graphical interpretation of a pair of linear equations, identify different types of lines, and understand how graphs help determine the number of solutions.
What You Will Learn?
✔ Graphical Representation of Linear Equations
✔ Intersecting Lines
✔ Parallel Lines
✔ Coincident Lines
✔ Graphical Meaning of Solutions
✔ Board Exam Concepts
Why This Topic Is Important?
Graphical representation helps students visualize linear equations and understand why different systems have different numbers of solutions.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
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Q1. Every linear equation in two variables represents:
A) A Circle
B) A Straight Line
C) A Parabola
D) A Curve
Answer:
$$\text{A Straight Line}$$
Useful Formula for this Question:
General Form:
$$ax+by+c=0$$
Concept Behind This Question:
Every linear equation in two variables forms a straight line on a graph.
Solution:
A linear equation has variables of degree:
$$1$$
Its graph is always a straight line.
Therefore, the correct answer is:
$$\text{A Straight Line}$$
Exam Tip:
Whenever you see a linear equation, immediately think of a straight line.
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Q2. If two straight lines intersect at exactly one point, then the pair of linear equations has:
A) No Solution
B) One Unique Solution
C) Infinitely Many Solutions
D) Four Solutions
Answer:
$$\text{One Unique Solution}$$
Useful Formula for this Question:
Intersecting lines have exactly one common point.
Concept Behind This Question:
The point of intersection satisfies both equations.
Solution:
Since both lines meet at only one point, there is only one pair of values:
$$x,\ y$$
that satisfies both equations.
Therefore, the correct answer is:
$$\text{One Unique Solution}$$
Exam Tip:
One intersection means one solution.
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Q3. If two straight lines never intersect, then they are:
A) Coincident Lines
B) Intersecting Lines
C) Parallel Lines
D) Perpendicular Lines
Answer:
$$\text{Parallel Lines}$$
Useful Formula for this Question:
Parallel lines never meet.
Concept Behind This Question:
Parallel lines maintain the same distance from each other.
Solution:
Since the lines never intersect, they have no common point.
Hence, they are:
$$\text{Parallel Lines}$$
Therefore, the correct answer is:
$$\text{Parallel Lines}$$
Exam Tip:
Parallel lines always have no graphical solution.
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Q4. If two lines completely overlap each other, they are called:
A) Parallel Lines
B) Intersecting Lines
C) Coincident Lines
D) Perpendicular Lines
Answer:
$$\text{Coincident Lines}$$
Useful Formula for this Question:
Coincident lines have every point in common.
Concept Behind This Question:
Both equations represent exactly the same straight line.
Solution:
When one line lies exactly on top of the other, every point on one line also lies on the second line.
Therefore, such lines are called:
$$\text{Coincident Lines}$$
Hence, the correct answer is:
$$\text{Coincident Lines}$$
Exam Tip:
Coincident lines represent infinitely many common points.
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Q5. Which of the following graphical situations represents infinitely many solutions?
A) Two Parallel Lines
B) Two Intersecting Lines
C) Two Coincident Lines
D) Two Perpendicular Lines
Answer:
$$\text{Two Coincident Lines}$$
Useful Formula for this Question:
Coincident lines have infinitely many common points.
Concept Behind This Question:
Every common point is a solution.
Solution:
Coincident lines overlap completely.
Therefore, every point on the line satisfies both equations.
Hence, there are infinitely many solutions.
Therefore, the correct answer is:
$$\text{Two Coincident Lines}$$
Exam Tip:
Remember the pattern:
One intersection → One solution
No intersection → No solution
Complete overlap → Infinite solutions
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Important Formulas and Concepts
General Form:
$$ax+by+c=0$$
Graph of a Linear Equation:
Straight Line
Intersecting Lines:
One common point
One Unique Solution
Parallel Lines:
No common point
No Solution
Coincident Lines:
Infinitely many common points
Infinitely Many Solutions
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FAQs
Q. Why is the graph of a linear equation always a straight line?
Answer:
Because the highest power of each variable is:
$$1$$
Q. What is the solution of two linear equations graphically?
Answer:
The common point where both graphs satisfy the equations.
Q. Why do coincident lines have infinitely many solutions?
Answer:
Because every point on the line satisfies both equations.
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Common Mistakes Students Make
❌ Confusing parallel and coincident lines.
❌ Assuming intersecting lines have two solutions.
❌ Forgetting that every linear equation represents a straight line.
❌ Mixing graphical solutions with algebraic methods.
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Quick Revision Notes
✔ Linear equation → Straight line.
✔ Intersecting lines → One unique solution.
✔ Parallel lines → No solution.
✔ Coincident lines → Infinitely many solutions.
✔ Common point of graphs = Solution of the equations.
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Conclusion:
These Class 10 Maths Chapter 3 MCQs strengthen the understanding of graphical representation of pair of linear equations in two variables. Mastering these concepts will make graphical and algebraic solution methods much easier in the upcoming practice sets.
Related links
- 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 graphical representation of polynomials – Part 12
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials ) – Part 11
- Class 10 Maths Chapter 2 Polynomials zeroes of polynomials – Part 10
- Class 10 Maths Chapter 2 Polynomials formation – Part 9
- Class 10 Maths Chapter 2 Forming Quadratic Polynomials – Part 8
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
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