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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, graphs, intercepts, equations of lines, and application-based 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: 14
Difficulty Level: 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 when it satisfies the given equation. The graph of a linear equation in two variables is a straight line containing infinitely many solution points.
This Practice Set 14 contains 5 fresh and slightly challenging MCQs based on important concepts such as solutions, coefficients, intercepts, graphs, and equations of lines.
What You Will Learn
✔ Verifying ordered pairs
✔ Finding unknown coefficients
✔ Finding intercepts
✔ Identifying equations from conditions
✔ Understanding graphical representation
✔ Applying algebraic reasoning
Why This Topic Is Important
Linear equations in two variables develop the ability to connect algebraic equations with geometrical representations. These concepts are important 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 the point ((-2,4)) lies on the equation
$$3x+ky=10,$$
then the value of (k) is:
A) (1)
B) (2)
C) (3)
D) (4)
Answer:
C) (4)
Useful Concept
A point lies on a line if its coordinates satisfy the equation.
Solution
Given:
$$3x+ky=10$$
The point is:
$$(-2,4)$$
Therefore:
$$x=-2,\quad y=4$$
Substitute:
$$3(-2)+4k=10$$
$$-6+4k=10$$
Adding 6:
$$4k=16$$
Therefore:
$$k=4$$
Hence, the correct answer is:
D) (4)
Correction: The numerical answer is (4), so the correct option is D.
Q2. Which of the following ordered pairs is not a solution of
$$5x-2y=16?$$
A) ((4,2))
B) ((2,-3))
C) ((0,-8))
D) ((6,7))
Answer:
D) ((6,7))
Useful Concept
Substitute each ordered pair into the equation to determine whether it satisfies the equation.
Solution
Given:
$$5x-2y=16$$
For ((4,2)):
$$5(4)-2(2)=20-4=16$$
So it is a solution.
For ((2,-3)):
$$5(2)-2(-3)=10+6=16$$
So it is a solution.
For ((0,-8)):
$$5(0)-2(-8)=16$$
So it is a solution.
For ((6,7)):
$$5(6)-2(7)=30-14=16$$
This is also a solution.
Therefore, the original options contain no incorrect pair.
Corrected Q2
Which of the following ordered pairs is not a solution of:
$$5x-2y=16?$$
A) ((4,2))
B) ((2,-3))
C) ((0,-8))
D) ((6,8))
For D:
$$5(6)-2(8)=30-16=14$$
Since:
$$14\ne16$$
((6,8)) is not a solution.
Hence, the correct answer is:
D) ((6,8))
Q3. The equation
$$4x+3y=24$$
cuts the coordinate axes at the points:
A) ((6,0)) and ((0,8))
B) ((8,0)) and ((0,6))
C) ((4,0)) and ((0,3))
D) ((3,0)) and ((0,4))
Answer:
A) ((6,0)) and ((0,8))
Useful Concept
For the (x)-intercept, put (y=0).
For the (y)-intercept, put (x=0).
Solution
Given:
$$4x+3y=24$$
(x)-intercept
Put:
$$y=0$$
Then:
$$4x=24$$
Therefore:
$$x=6$$
So the (x)-intercept is:
$$(6,0)$$
(y)-intercept
Put:
$$x=0$$
Then:
$$3y=24$$
Therefore:
$$y=8$$
So the (y)-intercept is:
$$(0,8)$$
Hence, the correct answer is:
A) ((6,0)) and ((0,8))
Q4. Which of the following equations represents a line passing through both points ((0,6)) and ((3,0))?
A) (2x+y=6)
B) (x+2y=6)
C) (2x+3y=6)
D) (3x+y=6)
Answer:
A) (2x+y=6)
Useful Concept
The required equation must be satisfied by both given points.
Solution
Check option A:
$$2x+y=6$$
For ((0,6)):
$$2(0)+6=6$$
Correct.
For ((3,0)):
$$2(3)+0=6$$
Correct.
Therefore, both points lie on:
$$2x+y=6$$
Hence, the correct answer is:
A) (2x+y=6)
Q5. If a linear equation has (x=3) for every value of (y), then its graph is:
A) A horizontal line
B) A vertical line
C) The (x)-axis
D) The (y)-axis
Answer:
B) A vertical line
Useful Concept
An equation of the form:
$$x=a$$
represents a vertical line parallel to the (y)-axis.
Solution
Given:
$$x=3$$
Here, the (x)-coordinate remains fixed at 3 while (y) can take any real value.
For example:
$$(3,0),\quad(3,2),\quad(3,-5)$$
all lie on this line.
Therefore, the graph is a vertical straight line parallel to the (y)-axis.
Hence, the correct answer is:
B) A vertical line
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 horizontal line parallel to the (x)-axis.
Vertical Line
$$x=a$$
represents a vertical line parallel to the (y)-axis.
Line Through Origin
$$ax+by=0$$
represents a line passing through the origin.
Related Practice Questions
Q1. If ((2,-4)) is a solution of:
$$3x+ky=10,$$
find (k).
Q2. Check whether ((3,-1)) satisfies:
$$2x-y=7$$
Q3. Find the intercepts of:
$$5x+2y=20$$
Q4. Find the equation of the line passing through ((0,8)) and ((4,0)).
Q5. What type of line does (x=-5) represent?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((3,2)) satisfies:
$$2x+ky=10$$
Q2. Find the (x)-intercept of:
$$5x+2y=20$$
Q3. Find the (y)-intercept of:
$$3x+4y=12$$
Q4. Which equation represents a vertical line?
A) (y=7)
B) (x=7)
C) (x+y=7)
D) (2x+y=7)
Q5. Does the point ((2,4)) lie on:
$$x+y=6$$
Exam Tips
✔ Always substitute coordinates carefully.
✔ Remember that (x=a) represents a vertical line.
✔ Remember that (y=b) represents a horizontal line.
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ When identifying an equation from two points, verify both points.
✔ Check 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:
$$x=a$$
✔ Line through origin:
$$ax+by=0$$
Common Mistakes Students Make
❌ Confusing (x)- and (y)-intercepts.
❌ Forgetting to substitute negative values correctly.
❌ Assuming (x=a) is a horizontal line.
❌ Assuming (y=b) is a vertical line.
❌ Checking only one point when an equation must pass through two points.
❌ Making arithmetic errors while simplifying.
Key Takeaways
✔ A linear equation in two variables is represented by a straight line.
✔ An ordered pair satisfying the equation is a solution.
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
✔ The (x)-intercept is obtained by putting (y=0).
✔ The (y)-intercept is obtained by putting (x=0).
✔ An equation of the form (ax+by=0) passes through the origin.
FAQs
Q. What is the standard form of a linear equation in two variables?
Answer:
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Q. What does (x=3) represent?
Answer:
It represents a vertical line parallel to the (y)-axis.
Q. What does (y=3) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
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).
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, coefficients, intercepts, equations of lines, and graphical concepts.
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