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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: 15
Difficulty Level: Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is generally written in the form:
$$ax+by+c=0$$
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 a linear equation if it 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 15 contains 5 fresh and challenging MCQs covering solutions, coefficients, intercepts, equations of lines, and graphical concepts.
What You Will Learn
✔ Verifying ordered pairs
✔ Finding unknown coefficients
✔ Finding intercepts
✔ Identifying equations from given points
✔ Understanding graphical representation
✔ Applying linear equations to practical situations
Why This Topic Is Important
Linear equations in two variables are an important foundation for algebra and coordinate geometry. They help students understand relationships between two quantities and develop logical and graphical 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 the point ((3,-2)) lies on the equation
$$2x+ky=10,$$
then the value of (k) is:
A) (-2)
B) (-1)
C) (1)
D) (2)
Answer:
B) (-1)
Useful Concept
If a point lies on the graph of an equation, its coordinates must satisfy the equation.
Solution
Given:
$$2x+ky=10$$
The point is:
$$(3,-2)$$
Therefore:
$$x=3,\quad y=-2$$
Substituting:
$$2(3)+k(-2)=10$$
$$6-2k=10$$
Subtracting 6:
$$-2k=4$$
Therefore:
$$k=-2$$
Hence, the correct answer is:
A) (-2)
Q2. Which of the following ordered pairs is not a solution of
$$3x+2y=12?$$
A) ((0,6))
B) ((2,3))
C) ((4,0))
D) ((3,2))
Answer:
D) ((3,2))
Useful Concept
An ordered pair is a solution only if its coordinates satisfy the given equation.
Solution
Given:
$$3x+2y=12$$
Option A: ((0,6))
$$3(0)+2(6)=12$$
So it is a solution.
Option B: ((2,3))
$$3(2)+2(3)=6+6=12$$
So it is a solution.
Option C: ((4,0))
$$3(4)+2(0)=12$$
So it is a solution.
Option D: ((3,2))
$$3(3)+2(2)=9+4=13$$
Since:
$$13\ne12$$
((3,2)) is not a solution.
Hence, the correct answer is:
D) ((3,2))
Q3. The (x)-intercept and (y)-intercept of the equation
$$4x+5y=20$$
are respectively:
A) (4) and (5)
B) (5) and (4)
C) (20) and (20)
D) (2) and (4)
Answer:
B) (5) and (4)
Useful Concept
To find the (x)-intercept, put:
$$y=0$$
To find the (y)-intercept, put:
$$x=0$$
Solution
Given:
$$4x+5y=20$$
Finding the (x)-intercept
Put:
$$y=0$$
Then:
$$4x=20$$
Therefore:
$$x=5$$
So the (x)-intercept is:
$$(5,0)$$
Finding the (y)-intercept
Put:
$$x=0$$
Then:
$$5y=20$$
Therefore:
$$y=4$$
So the (y)-intercept is:
$$(0,4)$$
Hence, the correct answer is:
B) (5) and (4)
Q4. Which of the following equations represents the line passing through the points
$$(0,7)$$
and:
$$(7,0)?$$
A) (x+y=7)
B) (x-y=7)
C) (2x+y=7)
D) (x+2y=7)
Answer:
A) (x+y=7)
Useful Concept
The equation must be satisfied by both given points.
Solution
Consider:
$$x+y=7$$
For the point ((0,7)):
$$0+7=7$$
So the point lies on the line.
For the point ((7,0)):
$$7+0=7$$
So this point also lies on the line.
Therefore, the required equation is:
$$x+y=7$$
Hence, the correct answer is:
A) (x+y=7)
Q5. A taxi charges a fixed amount of ₹50 and ₹10 per kilometre. If (x) represents the number of kilometres travelled and (y) represents the total fare, which equation represents the relationship between (x) and (y)?
A) (y=50x+10)
B) (y=10x+50)
C) (y=60x)
D) (x=10y+50)
Answer:
B) (y=10x+50)
Useful Concept
Total cost:
$$\text{Fixed charge}+\text{Cost per kilometre}\times\text{Distance}$$
Solution
The fixed charge is:
$$₹50$$
The charge per kilometre is:
$$₹10$$
If the distance travelled is (x) km, then the variable charge is:
$$10x$$
Therefore, the total fare (y) is:
$$y=50+10x$$
or:
$$y=10x+50$$
Hence, the correct answer is:
B) (y=10x+50)
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
An equation of the form:
$$ax+by=0$$
represents a line passing through the origin.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. If ((4,-1)) is a solution of:
$$kx+3y=9,$$
find (k).
Q2. Check whether ((2,5)) satisfies:
$$3x+y=11$$
Q3. Find the (x)-intercept of:
$$5x+2y=25$$
Q4. Find the (y)-intercept of:
$$3x+4y=24$$
Q5. A fixed charge of ₹30 and a charge of ₹5 per item are represented by (x) items and total cost (y). Write the linear equation.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. If ((2,3)) is a solution of:
$$kx+2y=14,$$
find (k).
Q2. Find the (x)-intercept of:
$$3x+2y=18$$
Q3. Find the (y)-intercept of:
$$4x+5y=20$$
Q4. Which equation represents a line passing through the origin?
A) (x+y=5)
B) (2x-3y=0)
C) (3x+y=8)
D) (x-y=4)
Q5. If a product costs ₹20 each and there is a fixed delivery charge of ₹50, write the equation for total cost (y) of (x) products.
Exam Tips
✔ Identify (a), (b), and (c) carefully when using standard form.
✔ Substitute ordered pairs carefully.
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ Verify both points when identifying an equation of a line.
✔ In word problems, clearly define the variables before forming the equation.
✔ Always check the final equation against the conditions given in the question.
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:
$$ax+by=0$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Confusing (x)-intercept with (y)-intercept.
❌ Forgetting to substitute both coordinates.
❌ Making sign errors with negative values.
❌ Confusing horizontal and vertical lines.
❌ Forgetting the fixed charge in application-based questions.
❌ Selecting an equation without checking the given conditions.
Key Takeaways
✔ A linear equation in two variables has the form:
$$ax+by+c=0$$
✔ Its solutions are ordered pairs.
✔ Its graph is a straight line.
✔ The (x)-intercept is found by putting (y=0).
✔ The (y)-intercept is found by putting (x=0).
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
✔ Linear equations can represent relationships between quantities in real-life situations.
FAQs
Q. What is a linear equation in two variables?
Answer:
It is an equation involving two variables (x) and (y), generally written as:
$$ax+by+c=0$$
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 is the graph of a linear equation in two variables?
Answer:
Its graph is a straight line.
Q. Can linear equations represent real-life situations?
Answer:
Yes. They can represent relationships involving fixed charges, rates, distances, quantities, costs, and many other situations.
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, graphs, and application-based problems.
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