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 and 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: 8
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is generally represented in the form:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
A pair ((x,y)) is called a solution of the equation if it satisfies the equation. The graph of a linear equation in two variables is a straight line containing infinitely many solution points.
This Practice Set 8 contains 5 fresh MCQs designed to strengthen students’ understanding of solutions, equations, intercepts, and graphical concepts.
What You Will Learn
✔ Finding unknown variables
✔ Checking ordered pairs
✔ Finding intercepts
✔ Identifying equations from points
✔ Understanding graphical representation
✔ Applying algebraic reasoning
Why This Topic Is Important
Linear equations in two variables form an important foundation for algebra and coordinate geometry. These concepts are frequently used in school examinations and help students develop systematic problem-solving skills.
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 ((2,4)) is a solution of the equation
$$3x+ky=14,$$
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, substitute its coordinates into the equation.
Solution
Given:
$$3x+ky=14$$
The solution is:
$$(2,4)$$
Therefore:
$$x=2,\quad y=4$$
Substituting:
$$3(2)+4k=14$$
$$6+4k=14$$
Subtract 6:
$$4k=8$$
Therefore:
$$k=2$$
Hence, the correct answer is:
B) (2)
Q2. Which of the following points lies on the line
$$2x+y=7?$$
A) ((1,5))
B) ((2,3))
C) ((3,2))
D) ((4,1))
Answer:
B) ((2,3))
Useful Concept
Substitute the coordinates of each point into the equation to determine whether it lies on the line.
Solution
Given:
$$2x+y=7$$
For option A:
$$2(1)+5=7$$
So ((1,5)) also satisfies the equation.
Therefore, the question has more than one correct answer.
To maintain a 100% valid MCQ, we correct the options.
Corrected Q2
Which of the following points lies on the line:
$$2x+y=7?$$
A) ((1,4))
B) ((2,3))
C) ((3,3))
D) ((4,2))
Check A:
$$2(1)+4=6\ne7$$
Check B:
$$2(2)+3=7$$
Therefore, B satisfies the equation.
Check C:
$$2(3)+3=9\ne7$$
Check D:
$$2(4)+2=10\ne7$$
Hence, the correct answer is:
B) ((2,3))
Q3. The (x)-intercept of the equation
$$5x+2y=20$$
is:
A) (2)
B) (4)
C) (5)
D) (10)
Answer:
B) (4)
Useful Concept
At the (x)-intercept:
$$y=0$$
Solution
Given:
$$5x+2y=20$$
Put:
$$y=0$$
Then:
$$5x+2(0)=20$$
$$5x=20$$
Therefore:
$$x=4$$
Hence, the (x)-intercept is:
$$(4,0)$$
Therefore, the correct answer is:
B) (4)
Q4. The equation
$$y=-3$$
represents:
A) A line parallel to the (x)-axis
B) A line parallel to the (y)-axis
C) The (x)-axis
D) The (y)-axis
Answer:
A) A line parallel to the (x)-axis
Useful Concept
An equation of the form:
$$y=b$$
represents a horizontal line parallel to the (x)-axis.
Solution
Given:
$$y=-3$$
Here, the (y)-coordinate remains constant at (-3), while (x) can take any real value.
Some points on the line are:
$$(-2,-3)$$
$$(0,-3)$$
$$(2,-3)$$
$$(5,-3)$$
All these points have the same (y)-coordinate.
Therefore, they form a horizontal straight line parallel to the (x)-axis.
Hence, the correct answer is:
A) A line parallel to the (x)-axis
Q5. Which equation represents the line passing through the points
$$(0,6)$$
and:
$$(3,0)?$$
A) (2x+y=6)
B) (x+2y=6)
C) (2x-y=6)
D) (x+y=3)
Answer:
A) (2x+y=6)
Useful Concept
The equation of the line must be satisfied by both given points.
Solution
We are given:
$$(0,6)$$
and:
$$(3,0)$$
Check option A:
$$2x+y=6$$
For ((0,6)):
$$2(0)+6=6$$
So the first point satisfies the equation.
For ((3,0)):
$$2(3)+0=6$$
So the second point also satisfies the equation.
Therefore, the line passes through both points.
Hence, the correct answer is:
A) (2x+y=6)
Important Concepts
Standard Form
$$ax+by+c=0$$
Solution
An ordered pair ((x,y)) satisfying the equation is called a solution.
(x)-Intercept
Put:
$$y=0$$
(y)-Intercept
Put:
$$x=0$$
Horizontal Line
$$y=b$$
represents a line parallel to the (x)-axis.
Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. If ((3,2)) is a solution of:
$$kx+4y=17,$$
find (k).
Q2. Check whether ((4,1)) lies on:
$$2x+y=9$$
Q3. Find the (x)-intercept of:
$$3x+2y=18$$
Q4. Find the (y)-intercept of:
$$4x+3y=12$$
Q5. Write the equation of the line passing through ((0,5)) and ((5,0)).
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((2,3)) is a solution of:
$$kx+y=11$$
Q2. Find the (x)-intercept of:
$$4x+y=16$$
Q3. Find the (y)-intercept of:
$$2x+3y=12$$
Q4. Does ((3,2)) satisfy:
$$x+2y=7?$$
Q5. What type of line is represented by:
$$y=8?$$
Exam Tips
✔ Always identify the values of (x) and (y) correctly.
✔ For checking a solution, substitute both coordinates.
✔ To find the (x)-intercept, put (y=0).
✔ To find the (y)-intercept, put (x=0).
✔ Remember:
$$y=b$$
represents a horizontal line.
✔ Verify the final answer in the original equation.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Horizontal line:
$$y=b$$
✔ Vertical line:
$$x=a$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Confusing (x)-intercept and (y)-intercept.
❌ Forgetting to substitute negative values correctly.
❌ Checking only one coordinate.
❌ Confusing horizontal and vertical lines.
❌ Making arithmetic errors while solving for an unknown variable.
❌ Choosing an answer without verifying it.
Key Takeaways
✔ A linear equation in two variables has the form:
$$ax+by+c=0$$
✔ Each 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:
The general form is:
$$ax+by+c=0$$
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. What does (y=-3) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
Q. What is the graph of a linear equation in two variables?
Answer:
It is a straight line.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide fresh NCERT-based practice on solutions, unknown coefficients, intercepts, equations of lines, and graphical concepts.
Related Links
- 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
- Class 9 Science Chapter 2 Is Matter Around Us Pure part-1
- Class 9 English Chapter 1 The Fun They Had part-7
- Class 9 Social Science Chapter 1: The French Revolution part-14
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
