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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. Learn the graphical method, coordinate plane, plotting points, and identifying solutions of linear equations 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 Level
Based On: NCERT Latest Syllabus
Introduction:
The graphical method is one of the simplest ways to solve a pair of linear equations in two variables. In this method, each equation is represented by a straight line on the Cartesian plane. The point where the two lines intersect gives the solution of the pair of equations.
Before learning algebraic methods such as substitution, elimination, and cross multiplication, every student should understand how to plot points correctly and draw straight lines on a graph. This graphical understanding builds strong conceptual clarity and helps students visualize why some systems have one solution, no solution, or infinitely many solutions.
In this practice set, students will focus on the graphical method, plotting points, and interpreting graphs based on NCERT concepts.
What You Will Learn?
✔ Cartesian Coordinate Plane
✔ Plotting Ordered Pairs
✔ Graphical Method
✔ Solution of Linear Equations
✔ Intersection Point
✔ Board Exam Concepts
Why This Topic Is Important?
The graphical method develops visual understanding and strengthens the foundation for algebraic solution methods.
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. In the graphical method, the solution of a pair of linear equations is:
Question Difficulty:
🟢 Easy
A) The midpoint of the graph
B) The point where the two lines intersect
C) The highest point on the graph
D) The origin only
Answer:
$$\text{The point where the two lines intersect}$$
Useful Formula for this Question:
Solution = Common point of both lines.
Concept Behind This Question:
The common point satisfies both equations simultaneously.
Solution:
When two graphs intersect, the coordinates of the intersection satisfy both equations.
Therefore, the solution is:
$$\text{The point where the two lines intersect}$$
Hence, the correct answer is:
$$\text{The point where the two lines intersect}$$
Exam Tip:
Always look for the common point while using the graphical method.
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Q2. Before drawing the graph of a linear equation, we first need:
Question Difficulty:
🟢 Easy
A) Only one point
B) At least two points
C) Five points
D) Ten points
Answer:
$$\text{At least two points}$$
Useful Formula for this Question:
A straight line is uniquely determined by two distinct points.
Concept Behind This Question:
Two points are sufficient to draw a straight line.
Solution:
To plot a straight line accurately, at least two points satisfying the equation are required.
Therefore, the correct answer is:
$$\text{At least two points}$$
Exam Tip:
Although two points are enough, plotting a third point helps verify accuracy.
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Q3. Which of the following is an ordered pair?
Question Difficulty:
🟢 Easy
A) $$3+4$$
B) $$(2,\ 5)$$
C) $$2:5$$
D) $$2-5$$
Answer:
$$(2,\ 5)$$
Useful Formula for this Question:
Ordered Pair:
$$(x,\ y)$$
Concept Behind This Question:
The first value represents the x-coordinate and the second represents the y-coordinate.
Solution:
An ordered pair is always written as:
$$(x,\ y)$$
Among the given options:
$$(2,\ 5)$$
is the correct ordered pair.
Hence, the correct answer is:
$$(2,\ 5)$$
Exam Tip:
Always write the x-coordinate first, followed by the y-coordinate.
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Q4. The point where the x-axis and y-axis intersect is called:
Question Difficulty:
🟢 Easy
A) Quadrant
B) Origin
C) Intercept
D) Coordinate
Answer:
$$\text{Origin}$$
Useful Formula for this Question:
Origin:
$$(0,\ 0)$$
Concept Behind This Question:
The origin is the reference point of the Cartesian plane.
Solution:
The x-axis and y-axis meet at:
$$(0,\ 0)$$
This point is called the:
$$\text{Origin}$$
Therefore, the correct answer is:
$$\text{Origin}$$
Exam Tip:
The origin always has coordinates:
$$(0,\ 0)$$
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Q5. If two linear equations have one common point on the graph, then the system is:
Question Difficulty:
🟡 Medium
A) Inconsistent
B) Dependent
C) Consistent with a Unique Solution
D) Impossible
Answer:
$$\text{Consistent with a Unique Solution}$$
Useful Formula for this Question:
Intersecting lines ⟶ One Unique Solution.
Concept Behind This Question:
A common point indicates exactly one solution satisfying both equations.
Solution:
Since both lines intersect at exactly one point, the pair of equations has one unique solution.
Such a system is called:
$$\text{Consistent with a Unique Solution}$$
Therefore, the correct answer is:
$$\text{Consistent with a Unique Solution}$$
Exam Tip:
Remember:
Consistent → At least one solution.
Inconsistent → No solution.
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Important Formulas and Concepts
General Form:
$$ax+by+c=0$$
Ordered Pair:
$$(x,\ y)$$
Origin:
$$(0,\ 0)$$
Solution by Graphical Method:
Intersection point of the two lines.
Straight Line:
Requires at least two distinct points.
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FAQs
Q. Why are two points enough to draw a straight line?
Answer:
Because one unique straight line passes through two distinct points.
Q. What is the graphical solution of two linear equations?
Answer:
The coordinates of their common intersection point.
Q. What is the origin?
Answer:
The point:
$$(0,\ 0)$$
where the x-axis and y-axis intersect.
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Common Mistakes Students Make
❌ Interchanging x-coordinate and y-coordinate.
❌ Plotting points incorrectly on the graph.
❌ Joining plotted points with a curved line instead of a straight line.
❌ Assuming the origin is always the solution.
❌ Forgetting that two points are sufficient to draw a straight line.
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Quick Revision Notes
✔ Ordered Pair:
$$(x,\ y)$$
✔ Origin:
$$(0,\ 0)$$
✔ Two points determine one straight line.
✔ Graphical solution = Intersection point.
✔ One common point → One unique solution.
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Conclusion:
These Class 10 Maths Chapter 3 MCQs help students build a strong understanding of the graphical method for solving pair of linear equations in two variables. Mastering these concepts prepares students for graph-based questions and lays the foundation for algebraic methods introduced later in the chapter.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two variables part-3
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-2
- 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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