Welcome To My School Study
Practice Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions based on the NCERT syllabus. Solve fresh, exam-oriented MCQs on linear equations, solutions, graphs, intercepts, and ordered pairs.
Do You Know
Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 9
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is generally written as:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
An ordered pair ((x,y)) is called a solution of the equation if it satisfies the equation. Since a linear equation in two variables generally has infinitely many solutions, its graph is a straight line.
This Practice Set 9 contains 5 fresh MCQs covering important concepts such as solutions, coefficients, intercepts, equations of lines, and graphical interpretation.
What You Will Learn
✔ Finding unknown coefficients
✔ Verifying ordered pairs
✔ Finding (x)- and (y)-intercepts
✔ Identifying equations from given points
✔ Understanding horizontal and vertical lines
✔ Applying substitution
Why This Topic Is Important
Linear equations in two variables provide the foundation for coordinate geometry and algebra. They help students understand the relationship between two quantities and are important for solving various mathematical problems.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ NCERT-Based Practice
✔ Mathematics Revision
Q1. If ((3,4)) is a solution of the equation
$$2x+ky=14,$$
then the value of (k) is:
A) (1)
B) (2)
C) (3)
D) (4)
Answer:
B) (2)
Useful Concept
If an ordered pair is a solution, substituting its coordinates into the equation must make the equation true.
Solution
Given:
$$2x+ky=14$$
The solution is:
$$(3,4)$$
Therefore:
$$x=3,\quad y=4$$
Substitute:
$$2(3)+4k=14$$
$$6+4k=14$$
$$4k=8$$
Therefore:
$$k=2$$
Hence, the correct answer is:
B) (2)
Q2. Which of the following points lies on the line
$$3x+2y=12?$$
A) ((2,3))
B) ((4,0))
C) ((0,6))
D) ((2,2))
Answer:
A) ((2,3))
Useful Concept
To check whether a point lies on a line, substitute its coordinates into the equation.
Solution
Given:
$$3x+2y=12$$
For option A:
$$(x,y)=(2,3)$$
Substitute:
$$3(2)+2(3)$$
$$=6+6$$
$$=12$$
Therefore, ((2,3)) satisfies the equation.
Check option B:
$$3(4)+2(0)=12$$
This also satisfies the equation.
Therefore, the original question contains two correct options.
To maintain a valid MCQ, we use a corrected option.
Corrected Q2
Which of the following points lies on the line:
$$3x+2y=12?$$
A) ((2,3))
B) ((1,3))
C) ((3,2))
D) ((2,2))
Check A:
$$6+6=12$$
Correct.
Check B:
$$3+6=9\ne12$$
Check C:
$$9+4=13\ne12$$
Check D:
$$6+4=10\ne12$$
Therefore, the correct answer is:
A) ((2,3))
Q3. What is the (y)-intercept of the equation
$$2x+3y=18?$$
A) (3)
B) (6)
C) (9)
D) (18)
Answer:
B) (6)
Useful Concept
At the (y)-intercept:
$$x=0$$
Solution
Given:
$$2x+3y=18$$
Put:
$$x=0$$
Then:
$$2(0)+3y=18$$
$$3y=18$$
Therefore:
$$y=6$$
Hence, the (y)-intercept is:
$$(0,6)$$
Therefore, the correct answer is:
B) (6)
Q4. Which equation represents a line parallel to the (y)-axis?
A) (y=5)
B) (y=-2)
C) (x=4)
D) (x+y=4)
Answer:
C) (x=4)
Useful Concept
An equation of the form:
$$x=a$$
represents a vertical line parallel to the (y)-axis.
Solution
Consider:
$$x=4$$
Here, the value of (x) remains constant at 4, while (y) can take any real value.
Some points on this line are:
$$(4,0)$$
$$(4,2)$$
$$(4,-3)$$
All these points have the same (x)-coordinate.
Therefore, they form a vertical line parallel to the (y)-axis.
Hence, the correct answer is:
C) (x=4)
Q5. The equation of a line passing through ((0,8)) and ((4,0)) is:
A) (x+y=8)
B) (2x+y=8)
C) (x+2y=8)
D) (2x-y=8)
Answer:
B) (2x+y=8)
Useful Concept
The equation of the line must be satisfied by both given points.
Solution
Given points:
$$(0,8)$$
and:
$$(4,0)$$
Check option B:
$$2x+y=8$$
For ((0,8)):
$$2(0)+8=8$$
Correct.
For ((4,0)):
$$2(4)+0=8$$
Correct.
Therefore, both points lie on:
$$2x+y=8$$
Hence, the correct answer is:
B) (2x+y=8)
Important Concepts
Standard Form
$$ax+by+c=0$$
Solution
An ordered pair ((x,y)) satisfying the equation is a solution.
(x)-Intercept
Put:
$$y=0$$
(y)-Intercept
Put:
$$x=0$$
Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Horizontal Line
$$y=b$$
represents a line parallel to the (x)-axis.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. If ((2,3)) is a solution of:
$$kx+2y=12,$$
find (k).
Q2. Check whether ((3,2)) lies on:
$$2x+y=8$$
Q3. Find the (x)-intercept of:
$$4x+2y=16$$
Q4. Find the (y)-intercept of:
$$3x+5y=15$$
Q5. Write the equation of the line passing through ((0,7)) and ((7,0)).
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((2,4)) is a solution of:
$$3x+ky=14$$
Q2. Find the (x)-intercept of:
$$5x+y=20$$
Q3. Find the (y)-intercept of:
$$2x+4y=16$$
Q4. What type of line is represented by:
$$x=-5?$$
Q5. Does ((3,1)) satisfy:
$$2x+y=7?$$
Exam Tips
✔ Substitute coordinates carefully.
✔ For the (x)-intercept, set (y=0).
✔ For the (y)-intercept, set (x=0).
✔ Remember that (x=a) is a vertical line.
✔ Remember that (y=b) is a horizontal line.
✔ Verify the final answer using the original equation.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Vertical line:
$$x=a$$
✔ Horizontal line:
$$y=b$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Confusing (x)-intercept and (y)-intercept.
❌ Forgetting to substitute negative values correctly.
❌ Confusing (x=a) with (y=a).
❌ Not checking both coordinates of an ordered pair.
❌ Making arithmetic errors during substitution.
❌ Selecting an MCQ option without verification.
Key Takeaways
✔ A linear equation in two variables has the form:
$$ax+by+c=0$$
✔ Its solution is represented by an ordered pair.
✔ A linear equation in two variables generally has infinitely many solutions.
✔ Its graph is a straight line.
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
FAQs
Q. What is the general form of a linear equation in two variables?
Answer:
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Q. How do we find the (x)-intercept?
Answer:
Put:
$$y=0$$
and solve for (x).
Q. How do we find the (y)-intercept?
Answer:
Put:
$$x=0$$
and solve for (y).
Q. Which equation represents a line parallel to the (y)-axis?
Answer:
An equation of the form:
$$x=a$$
represents a line parallel to the (y)-axis.
Q. Which equation represents a line parallel to the (x)-axis?
Answer:
An equation of the form:
$$y=b$$
represents a line parallel to the (x)-axis.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide fresh NCERT-based practice on unknown coefficients, ordered pairs, intercepts, equations of lines, and graphical concepts.
Related Links
- Class 9 Science Chapter 2 Is Matter Around Us Pure part-4
- Class 9 Social Science Chapter 1: The French Revolution part-17
- Class 9 Maths Chapter 4 Linear Equations in Two Variables part-8
- Class 9 Science Chapter 2 Is Matter Around Us Pure PART-3
- Class 9 Maths Chapter 4 Linear Equations in Two Variables PART-7
- Class 9 English Chapter 1 The Fun They Had part-9
- Class 9 Social Science Chapter 1: The French Revolution part-16
- Class 9 Science Chapter 2 Is Matter Around Us Pure part-2
- Class 9 Maths Chapter 4 Linear Equations in Two Variables part-6
- Class 9 English Chapter 1 The Fun They Had part-8
- Class 9 Social Science Chapter 1: The French Revolution part-15
- Class 9 Maths Chapter 4 Linear Equations in Two Variables part-5
Latest Posts
- Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry
- Class 10 Maths Chapter 5 -Arithmetic Progressions
- Class 7 Maths Chapter 5 – Parallel and Intersecting Lines
- Class 8 Maths Chapter 5 – Number Play
- Class 9 English Chapter 2 The Pot Maker
Join Our Other Communities
Instagram , Youtube , Facebook
