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 solutions, graphs, intercepts, equations of lines, and algebraic concepts.
Do You Know
Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 11
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is an equation of the form:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
The solution of a linear equation in two variables is an ordered pair ((x,y)) that satisfies the equation. Such an equation generally has infinitely many solutions, and its graph is a straight line.
This Practice Set 11 contains 5 fresh MCQs covering substitution, solutions, intercepts, equations of lines, and graphical interpretation.
What You Will Learn
✔ Finding unknown coefficients
✔ Checking whether ordered pairs are solutions
✔ Finding intercepts
✔ Identifying equations from given points
✔ Understanding lines parallel to coordinate axes
✔ Applying algebraic reasoning
Why This Topic Is Important
Linear equations in two variables are an important part of Class 9 Mathematics. They develop students’ algebraic and graphical understanding and provide a foundation for coordinate geometry and higher-level algebra.
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 ((-2,3)) is a solution of the equation
$$kx+2y=8,$$
then the value of (k) is:
A) (-1)
B) (-2)
C) (1)
D) (2)
Answer:
B) (-1)
Useful Concept
If an ordered pair is a solution, its coordinates must satisfy the given equation.
Solution
Given:
$$kx+2y=8$$
The point is:
$$(-2,3)$$
Therefore:
$$x=-2,\quad y=3$$
Substituting:
$$k(-2)+2(3)=8$$
$$-2k+6=8$$
Subtract 6:
$$-2k=2$$
Therefore:
$$k=-1$$
Hence, the correct answer is:
A) (-1)
Correction: The numerical answer is (-1), so the correct option is A, not B.
Q2. Which of the following points is not a solution of
$$2x+3y=12?$$
A) ((0,4))
B) ((3,2))
C) ((6,0))
D) ((2,3))
Answer:
D) ((2,3))
Useful Concept
Substitute each ordered pair into the equation. A point that does not satisfy the equation is not a solution.
Solution
Given:
$$2x+3y=12$$
For ((0,4)):
$$2(0)+3(4)=12$$
So it is a solution.
For ((3,2)):
$$2(3)+3(2)=6+6=12$$
So it is a solution.
For ((6,0)):
$$2(6)+3(0)=12$$
So it is a solution.
For ((2,3)):
$$2(2)+3(3)=4+9=13$$
Since:
$$13\ne12$$
((2,3)) is not a solution.
Hence, the correct answer is:
D) ((2,3))
Q3. The (x)-intercept of the equation
$$3x+4y=24$$
is:
A) (4)
B) (6)
C) (8)
D) (12)
Answer:
B) (8)
Useful Concept
At the (x)-intercept:
$$y=0$$
Solution
Given:
$$3x+4y=24$$
Put:
$$y=0$$
Then:
$$3x+4(0)=24$$
$$3x=24$$
Therefore:
$$x=8$$
Hence, the (x)-intercept is:
$$(8,0)$$
Therefore, the correct answer is:
C) (8)
Correction: The numerical answer is (8), so the correct option is C, not B.
Q4. Which of the following equations represents a line parallel to the (x)-axis?
A) (x=7)
B) (x=-3)
C) (y=5)
D) (x+y=5)
Answer:
C) (y=5)
Useful Concept
An equation of the form:
$$y=b$$
represents a horizontal line parallel to the (x)-axis.
Solution
Given:
$$y=5$$
The (y)-coordinate remains constant at 5, while (x) can have any real value.
For example, the points:
$$(0,5),\quad(2,5),\quad(-3,5)$$
all lie on this line.
Since the line is horizontal, it is parallel to the (x)-axis.
Hence, the correct answer is:
C) (y=5)
Q5. Which equation represents the line passing through the points
$$(1,2)$$
and:
$$(3,6)?$$
A) (2x-y=0)
B) (x-2y=0)
C) (2x+y=4)
D) (x+y=3)
Answer:
A) (2x-y=0)
Useful Concept
The equation of the line must be satisfied by both given points.
Solution
Consider:
$$2x-y=0$$
For the point ((1,2)):
$$2(1)-2=2-2=0$$
So ((1,2)) lies on the line.
For the point ((3,6)):
$$2(3)-6=6-6=0$$
So ((3,6)) also lies on the line.
Therefore, the required equation is:
$$2x-y=0$$
Hence, the correct answer is:
A) (2x-y=0)
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.
Number of Solutions
A linear equation in two variables generally has infinitely many solutions.
Related Practice Questions
Q1. If ((2,-1)) is a solution of:
$$3x+ky=10,$$
find (k).
Q2. Check whether ((4,1)) is a solution of:
$$2x+3y=11$$
Q3. Find the (x)-intercept of:
$$4x+3y=24$$
Q4. Find the (y)-intercept of:
$$5x+2y=20$$
Q5. Write the equation of the line passing through ((0,4)) and ((2,0)).
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((2,3)) satisfies:
$$kx+3y=12$$
Q2. Find the (x)-intercept of:
$$2x+y=10$$
Q3. Find the (y)-intercept of:
$$3x+2y=12$$
Q4. Which equation represents a line parallel to the (y)-axis?
A) (y=3)
B) (x=3)
C) (x+y=3)
D) (2x+y=3)
Q5. Check whether ((1,4)) lies on:
$$2x+y=6$$
Exam Tips
✔ Substitute coordinates carefully.
✔ Pay special attention to negative signs.
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ Remember that (y=b) represents a horizontal line.
✔ Remember that (x=a) represents a vertical 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
❌ Forgetting the sign of a negative coordinate.
❌ Confusing (x)-intercept and (y)-intercept.
❌ Treating (x=a) as a horizontal line.
❌ Treating (y=b) as a vertical line.
❌ Not verifying both points when identifying an equation.
❌ Making calculation errors during substitution.
Key Takeaways
✔ A linear equation in two variables has the form:
$$ax+by+c=0$$
✔ Its solutions are ordered pairs.
✔ It generally has infinitely many solutions.
✔ Its graph is a straight line.
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
✔ Intercepts are obtained by making the other coordinate zero.
FAQs
Q. What is a solution of a linear equation in two variables?
Answer:
An ordered pair ((x,y)) that satisfies the equation is called a solution.
Q. What is the (x)-intercept?
Answer:
The (x)-intercept is obtained by putting:
$$y=0$$
Q. What is the (y)-intercept?
Answer:
The (y)-intercept is obtained by putting:
$$x=0$$
Q. What does (y=b) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
Q. What does (x=a) represent?
Answer:
It represents a vertical line parallel to the (y)-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 ordered pairs, unknown coefficients, intercepts, equations of lines, and graphical interpretation.
Related Links
- Class 9 Science Chapter 2 Is Matter Around Us Pure part-6
- Class 9 History Chapter 2 Socialism in Europe and Russian Revolution part-1
- Class 9 English Chapter 2 The Pot Maker part-2
- Class 9 Maths Chapter 4 Linear Equations in Two Variables part-10
- Class 9 Science Chapter 2 Is Matter Around Us Pure part-5
- Class 9 Social Science Chapter 1: The French Revolution part-18
- Class 9 English Chapter 2 The Pot Maker part-1
- Class 9 Maths Chapter 4 Linear Equations in Two Variables part-9
Latest Posts
- Class 10 Science Chapter 2 Acids, Bases and Salts
- Class 9 Science Chapter 2 Is Matter Around Us Pure
- Class 7 Science Chapter 2 Nutrition in Animals
- Class 8 Science Chapter 2 Microorganisms Friend and Foe
- Class 8 History Chapter 2 From Trade to Territory
Join Our Other Communities
Instagram , Youtube , Facebook
