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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, coefficients, graphs, intercepts, and linear equations.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 6
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is an equation involving two variables in which the highest power of each variable is one. It can generally be written as:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
A pair of values ((x,y)) that satisfies the equation is called a solution. The graph of a linear equation in two variables is a straight line.
This Practice Set 6 contains 5 fresh MCQs designed to strengthen conceptual understanding of solutions, equations, intercepts, and graphical representation.
What You Will Learn
✔ Finding unknown coefficients
✔ Verifying solutions
✔ Finding intercepts
✔ Understanding equations of lines
✔ Identifying graphical properties
✔ Applying substitution
Why This Topic Is Important
Linear equations in two variables are an important foundation for algebra and coordinate geometry. Understanding their solutions and graphs helps students solve mathematical problems involving two related quantities.
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 ((2,5)) 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 of an equation, its coordinates must satisfy the equation.
Solution
Given:
$$3x+ky=16$$
The solution is:
$$(2,5)$$
Therefore:
$$x=2,\quad y=5$$
Substituting:
$$3(2)+k(5)=16$$
$$6+5k=16$$
Subtracting 6:
$$5k=10$$
Therefore:
$$k=2$$
Hence, the correct answer is:
B) (2)
Q2. Which of the following ordered pairs is a solution of
$$4x-3y=5?$$
A) ((2,1))
B) ((2,2))
C) ((1,-1))
D) ((3,2))
Answer:
A) ((2,1))
Useful Concept
To verify an ordered pair, substitute the values of (x) and (y) into the given equation.
Solution
Given:
$$4x-3y=5$$
For option A:
$$x=2,\quad y=1$$
Substituting:
$$4(2)-3(1)$$
$$=8-3$$
$$=5$$
Therefore, ((2,1)) satisfies the equation.
Check the other options:
For ((2,2)):
$$4(2)-3(2)=8-6=2\ne5$$
For ((1,-1)):
$$4(1)-3(-1)=4+3=7\ne5$$
For ((3,2)):
$$4(3)-3(2)=12-6=6\ne5$$
Hence, the correct answer is:
A) ((2,1))
Q3. The (y)-intercept of the equation
$$3x+4y=24$$
is:
A) (4)
B) (6)
C) (8)
D) (12)
Answer:
C) (6)
Useful Concept
At the (y)-intercept, the value of (x) is zero.
Therefore:
$$x=0$$
Solution
Given:
$$3x+4y=24$$
For the (y)-intercept:
$$x=0$$
Substituting:
$$3(0)+4y=24$$
$$4y=24$$
Therefore:
$$y=6$$
Hence, the (y)-intercept is:
$$(0,6)$$
Therefore, the correct answer is:
B) (6)
Note: The numerical value is (6), so the correct option should be B, not C.
Q4. Which equation represents a 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
An equation of a line must be satisfied by every point lying on that line.
Solution
We are given the points:
$$(0,7)$$
and:
$$(7,0)$$
Check option A:
$$x+y=7$$
For ((0,7)):
$$0+7=7$$
So the point satisfies the equation.
For ((7,0)):
$$7+0=7$$
So this point also satisfies the equation.
Therefore, the line passes through both given points.
Hence, the correct answer is:
A) (x+y=7)
Q5. If the equation
$$2x+5y=20$$
has (x=0), then the corresponding value of (y) is:
A) (2)
B) (4)
C) (5)
D) (10)
Answer:
B) (4)
Useful Concept
When (x=0), the corresponding point lies on the (y)-axis.
Solution
Given:
$$2x+5y=20$$
and:
$$x=0$$
Substituting:
$$2(0)+5y=20$$
$$5y=20$$
Therefore:
$$y=4$$
Hence, the corresponding point is:
$$(0,4)$$
Therefore, the correct answer is:
B) (4)
Important Concepts
Standard Form
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Solution
An ordered pair ((x,y)) satisfying the equation is called its solution.
(x)-Intercept
For the (x)-intercept:
$$y=0$$
(y)-Intercept
For the (y)-intercept:
$$x=0$$
Equation of a Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Equation of a Horizontal Line
$$y=b$$
represents a line parallel to the (x)-axis.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. If ((3,2)) is a solution of:
$$kx+2y=13,$$
find (k).
Q2. Check whether ((4,3)) is a solution of:
$$2x+y=11$$
Q3. Find the (x)-intercept of:
$$4x+3y=12$$
Q4. Find the (y)-intercept of:
$$5x+2y=10$$
Q5. Find the point where:
$$x+y=9$$
meets the (y)-axis.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. If ((2,3)) satisfies:
$$kx+y=11,$$
find (k).
Q2. Find the (x)-intercept of:
$$3x+y=15$$
Q3. Find the (y)-intercept of:
$$2x+5y=20$$
Q4. Check whether ((5,2)) satisfies:
$$x+2y=9$$
Q5. Which equation represents a line parallel to the (x)-axis?
Exam Tips
✔ Substitute the given values carefully.
✔ Keep track of negative signs.
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ Remember that every point on a line satisfies its equation.
✔ Check the final answer in the original equation whenever possible.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Ordered-pair solution:
$$(x,y)$$
✔ (x)-axis:
$$y=0$$
✔ (y)-axis:
$$x=0$$
✔ (x=a):
Vertical line.
✔ (y=b):
Horizontal line.
✔ Graph:
Straight line.
Common Mistakes Students Make
❌ Forgetting to substitute the value of (x) or (y).
❌ Using the wrong condition for intercepts.
❌ Confusing (x)-axis with (y)-axis.
❌ Ignoring negative signs.
❌ Writing the coordinates in reverse order.
❌ Selecting an option without checking it in the original equation.
Key Takeaways
✔ A linear equation in two variables has infinitely many solutions.
✔ Solutions are represented by ordered pairs.
✔ The (x)-intercept is obtained by putting (y=0).
✔ The (y)-intercept is obtained by putting (x=0).
✔ Every point on the graph satisfies the corresponding equation.
✔ The graph of a linear equation in two variables is a straight line.
FAQs
Q. How do we find the (x)-intercept?
Answer:
Put:
$$y=0$$
in the equation and find (x).
Q. How do we find the (y)-intercept?
Answer:
Put:
$$x=0$$
in the equation and find (y).
Q. What does (x=a) represent?
Answer:
It represents a vertical line parallel to the (y)-axis.
Q. What does (y=b) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
Q. How can we verify an ordered pair?
Answer:
Substitute its (x)- and (y)-coordinates into the equation. If the equation is satisfied, the ordered pair is a solution.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide fresh NCERT-based practice on coefficients, solutions, intercepts, and graphical concepts.
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