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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 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: 12
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.
A solution of such an equation is an ordered pair ((x,y)) that satisfies the equation. A linear equation in two variables generally has infinitely many solutions, and these solutions are represented graphically by points lying on a straight line.
This Practice Set 12 contains 5 fresh MCQs designed to test conceptual understanding, substitution, intercepts, and graphical interpretation.
What You Will Learn
✔ Finding unknown coefficients
✔ Verifying solutions
✔ Finding intercepts
✔ Identifying equations from given points
✔ Understanding graphs
✔ Applying linear equations to mathematical situations
Why This Topic Is Important
Linear equations in two variables help students understand relationships between two quantities. They also form an important foundation for coordinate geometry and later algebraic concepts.
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 ((4,2)) is a solution of the equation
$$3x+ky=16,$$
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, its coordinates satisfy the given equation.
Solution
Given:
$$3x+ky=16$$
The solution is:
$$(4,2)$$
Therefore:
$$x=4,\quad y=2$$
Substituting:
$$3(4)+2k=16$$
$$12+2k=16$$
$$2k=4$$
Therefore:
$$k=2$$
Hence, the correct answer is:
B) (2)
Q2. Which of the following points is a solution of
$$4x-y=9?$$
A) ((2,-1))
B) ((2,-2))
C) ((3,3))
D) ((1,-5))
Answer:
A) ((2,-1))
Useful Concept
Substitute the coordinates into the equation to verify whether the point is a solution.
Solution
Given:
$$4x-y=9$$
For option A:
$$x=2,\quad y=-1$$
Substitute:
$$4(2)-(-1)$$
$$=8+1$$
$$=9$$
Therefore, ((2,-1)) is a solution.
Check option B:
$$4(2)-(-2)=10\ne9$$
Option C:
$$4(3)-3=9$$
This is also a solution.
Therefore, the original options contain two correct answers.
Corrected Q2
Which of the following points is a solution of:
$$4x-y=9?$$
A) ((2,-1))
B) ((2,-2))
C) ((3,4))
D) ((1,-5))
Check A:
$$8+1=9$$
Correct.
Check B:
$$8+2=10\ne9$$
Check C:
$$12-4=8\ne9$$
Check D:
$$4-(-5)=9$$
Again, D is also a solution.
Therefore, we correct D as well.
Final Verified Q2
Which of the following points is a solution of:
$$4x-y=9?$$
A) ((2,-1))
B) ((2,-2))
C) ((3,4))
D) ((1,-4))
Check D:
$$4(1)-(-4)=8\ne9$$
Thus, only A satisfies the equation.
Hence, the correct answer is:
A) ((2,-1))
Q3. The (y)-intercept of the equation
$$5x+2y=20$$
is:
A) (2)
B) (4)
C) (5)
D) (10)
Answer:
B) (10)
Useful Concept
At the (y)-intercept:
$$x=0$$
Solution
Given:
$$5x+2y=20$$
Put:
$$x=0$$
Then:
$$5(0)+2y=20$$
$$2y=20$$
Therefore:
$$y=10$$
Hence, the (y)-intercept is:
$$(0,10)$$
Therefore, the correct answer is:
D) (10)
Correction: The numerical answer is (10), so the correct option is D, not B.
Q4. Which of the following equations represents a line passing through the origin?
A) (2x+3y=6)
B) (x-4y=0)
C) (3x+y=5)
D) (2x-y=7)
Answer:
B) (x-4y=0)
Useful Concept
The origin is:
$$(0,0)$$
An equation represents a line passing through the origin if ((0,0)) satisfies it.
Solution
Check option B:
$$x-4y=0$$
At the origin:
$$x=0,\quad y=0$$
Therefore:
$$0-4(0)=0$$
So the equation is satisfied.
Check option A:
$$2(0)+3(0)=0\ne6$$
Therefore, it does not pass through the origin.
Hence, the correct answer is:
B) (x-4y=0)
Q5. A line cuts the (x)-axis at (5) and the (y)-axis at (10). Which equation represents the line?
A) (2x+y=10)
B) (x+2y=10)
C) (2x+y=5)
D) (x+y=10)
Answer:
A) (2x+y=10)
Useful Concept
If a line has (x)-intercept (5) and (y)-intercept (10), it passes through:
$$(5,0)$$
and:
$$(0,10)$$
Solution
Check option A:
$$2x+y=10$$
For ((5,0)):
$$2(5)+0=10$$
Correct.
For ((0,10)):
$$2(0)+10=10$$
Correct.
Therefore, the required equation is:
$$2x+y=10$$
Hence, the correct answer is:
A) (2x+y=10)
Important Concepts
Standard Form
$$ax+by+c=0$$
Solution
An ordered pair ((x,y)) that satisfies the equation is a solution.
Origin
$$O=(0,0)$$
(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 ((2,5)) is a solution of:
$$kx+y=11,$$
find (k).
Q2. Check whether ((3,2)) lies on:
$$4x-y=10$$
Q3. Find the (x)-intercept of:
$$2x+5y=20$$
Q4. Find the (y)-intercept of:
$$3x+4y=12$$
Q5. Does the equation
$$3x-2y=0$$
pass through the origin?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find (k) if ((3,2)) is a solution of:
$$2x+ky=12$$
Q2. Find the (x)-intercept of:
$$4x+y=16$$
Q3. Find the (y)-intercept of:
$$3x+2y=18$$
Q4. Which equation passes through the origin?
A) (x+y=5)
B) (2x-3y=0)
C) (3x+y=7)
D) (x-2y=4)
Q5. What are the coordinates of the origin?
Exam Tips
✔ Remember that the origin is ((0,0)).
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ To check whether a line passes through the origin, substitute ((0,0)).
✔ Verify both intercepts when identifying an equation.
✔ Carefully handle negative signs during substitution.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ Origin:
$$(0,0)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Line through origin:
$$ax+by=0$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Forgetting that the origin is ((0,0)).
❌ Confusing the (x)-intercept with the (y)-intercept.
❌ Substituting the wrong coordinate as zero.
❌ Not checking both given points.
❌ Making sign errors while substituting negative values.
❌ Selecting an option without verifying it.
Key Takeaways
✔ A linear equation in two variables generally has the form:
$$ax+by+c=0$$
✔ Its solutions are ordered pairs.
✔ Its graph is a straight line.
✔ The origin is ((0,0)).
✔ A line passing through the origin can be written as:
$$ax+by=0$$
✔ The (x)-intercept is found by putting (y=0).
✔ The (y)-intercept is found by putting (x=0).
FAQs
Q. What is the origin?
Answer:
The origin is the point:
$$(0,0)$$
where the (x)-axis and (y)-axis intersect.
Q. How can we check whether a line passes through the origin?
Answer:
Substitute:
$$x=0,\quad y=0$$
If the equation is satisfied, the line passes through the origin.
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 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, coefficients, intercepts, equations passing through the origin, and graphical concepts.
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