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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, intercepts, graphs, equations of lines, and coordinate concepts.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 13
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is generally expressed 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 a solution of the equation if it satisfies the equation. A linear equation in two variables generally has infinitely many solutions, and its graph is a straight line.
This Practice Set 13 contains 5 fresh MCQs based on important concepts such as solutions, intercepts, equations of lines, and graphical interpretation.
What You Will Learn
✔ Finding unknown coefficients
✔ Verifying ordered pairs
✔ Finding intercepts
✔ Identifying equations from points
✔ Understanding lines through the origin
✔ Applying substitution
Why This Topic Is Important
Linear equations in two variables develop algebraic reasoning and graphical understanding. These concepts are useful in coordinate geometry and provide a foundation for more advanced topics in mathematics.
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
$$4x+ky=5,$$
then the value of (k) is:
A) (1)
B) (2)
C) (3)
D) (-1)
Answer:
B) (1)
Useful Concept
If an ordered pair is a solution, substituting its coordinates must satisfy the equation.
Solution
Given:
$$4x+ky=5$$
The point is:
$$(2,-3)$$
Therefore:
$$x=2,\quad y=-3$$
Substituting:
$$4(2)+k(-3)=5$$
$$8-3k=5$$
Subtract 8:
$$-3k=-3$$
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 does not lie on the line
$$x+2y=8?$$
A) ((0,4))
B) ((2,3))
C) ((4,2))
D) ((6,1))
Answer:
D) ((6,1))
Useful Concept
Substitute the coordinates of each point into the equation.
Solution
Given:
$$x+2y=8$$
For ((0,4)):
$$0+2(4)=8$$
So it lies on the line.
For ((2,3)):
$$2+2(3)=8$$
So it lies on the line.
For ((4,2)):
$$4+2(2)=8$$
So it lies on the line.
For ((6,1)):
$$6+2(1)=8$$
$$6+2=8$$
This also satisfies the equation.
Therefore, the original options do not contain an incorrect point.
Corrected Q2
Which of the following points does not lie on the line:
$$x+2y=8?$$
A) ((0,4))
B) ((2,3))
C) ((4,2))
D) ((5,2))
For D:
$$5+2(2)=9\ne8$$
Therefore, ((5,2)) does not lie on the line.
Hence, the correct answer is:
D) ((5,2))
Q3. The (x)-intercept and (y)-intercept of
$$3x+2y=12$$
are respectively:
A) (4) and (6)
B) (6) and (4)
C) (3) and (2)
D) (12) and (12)
Answer:
A) (4) and (6)
Useful Concept
For the (x)-intercept, put:
$$y=0$$
For the (y)-intercept, put:
$$x=0$$
Solution
Given:
$$3x+2y=12$$
(x)-intercept
Put:
$$y=0$$
Then:
$$3x=12$$
Therefore:
$$x=4$$
(y)-intercept
Put:
$$x=0$$
Then:
$$2y=12$$
Therefore:
$$y=6$$
Hence:
$$x\text{-intercept}=4$$
and:
$$y\text{-intercept}=6$$
Therefore, the correct answer is:
A) (4) and (6)
Q4. Which of the following equations represents a line passing through the origin?
A) (3x+2y=6)
B) (4x-y=0)
C) (2x+y=5)
D) (x-3y=7)
Answer:
B) (4x-y=0)
Useful Concept
The origin is:
$$(0,0)$$
An equation passes through the origin if ((0,0)) satisfies it.
Solution
Check option B:
$$4x-y=0$$
At:
$$x=0,\quad y=0$$
we get:
$$4(0)-0=0$$
Therefore, the equation is satisfied.
Thus, the line passes through the origin.
Check option A:
$$3(0)+2(0)=0\ne6$$
Therefore, it does not pass through the origin.
Hence, the correct answer is:
B) (4x-y=0)
Q5. The graph of the equation
$$y=4$$
is:
A) A line parallel to the (y)-axis
B) A line parallel to the (x)-axis
C) The (x)-axis
D) The (y)-axis
Answer:
B) 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:
$$y=4$$
The (y)-coordinate remains fixed at 4, while (x) can take any real value.
For example:
$$(0,4),\quad(2,4),\quad(-3,4)$$
are all points on the graph.
Since the (y)-coordinate is constant, the graph is a horizontal straight line.
Therefore, it is parallel to the (x)-axis.
Hence, the correct answer is:
B) A line parallel to the (x)-axis
Important Concepts
Standard Form
$$ax+by+c=0$$
Solution
An ordered pair ((x,y)) satisfying the equation is a solution.
Origin
$$(0,0)$$
(x)-Intercept
Put:
$$y=0$$
(y)-Intercept
Put:
$$x=0$$
Line Through Origin
An equation of the form:
$$ax+by=0$$
represents a line passing through the origin.
Horizontal Line
$$y=b$$
represents a line parallel to the (x)-axis.
Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Related Practice Questions
Q1. If ((3,-2)) is a solution of:
$$kx+2y=5,$$
find (k).
Q2. Check whether ((2,4)) lies on:
$$x+2y=10$$
Q3. Find the (x)-intercept of:
$$4x+3y=24$$
Q4. Find the (y)-intercept of:
$$2x+5y=20$$
Q5. Does the equation
$$5x+y=0$$
pass through the origin?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((2,3)) satisfies:
$$3x+ky=12$$
Q2. Find the (x)-intercept of:
$$2x+3y=12$$
Q3. Find the (y)-intercept of:
$$4x+2y=16$$
Q4. Which equation represents a horizontal line?
A) (x=5)
B) (y=5)
C) (x+y=5)
D) (2x+y=5)
Q5. Is ((1,3)) a solution of:
$$2x+y=5?$$
Exam Tips
✔ Substitute coordinates carefully.
✔ Remember the origin:
$$(0,0)$$
✔ For the (x)-intercept, set (y=0).
✔ For the (y)-intercept, set (x=0).
✔ An equation (y=b) represents a horizontal line.
✔ An equation (x=a) represents a vertical line.
✔ Always verify your final answer in the original equation.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ Origin:
$$(0,0)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Horizontal line:
$$y=b$$
✔ Vertical line:
$$x=a$$
✔ Line through origin:
$$ax+by=0$$
Common Mistakes Students Make
❌ Confusing the (x)-intercept and (y)-intercept.
❌ Forgetting to substitute both coordinates.
❌ Confusing horizontal and vertical lines.
❌ Forgetting that the origin is ((0,0)).
❌ Making sign errors while substituting negative values.
❌ Not verifying an equation using the given point.
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.
✔ (y=b) represents a horizontal line.
✔ (x=a) represents a vertical line.
✔ (ax+by=0) represents a line passing through the origin.
FAQs
Q. What is the graph of (y=4)?
Answer:
It is a horizontal line parallel to the (x)-axis.
Q. What is the graph of (x=4)?
Answer:
It is a vertical line parallel to the (y)-axis.
Q. How can we check whether a point lies on a line?
Answer:
Substitute its coordinates into the equation. If the equation is satisfied, the point lies on the line.
Q. What is the origin?
Answer:
The origin is:
$$(0,0)$$
Q. How do we find the (x)-intercept?
Answer:
Put:
$$y=0$$
and solve for (x).
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, coefficients, intercepts, lines through the origin, and graphical representation.
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