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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 MCQs on linear equations, solutions, graphs, intercepts, and ordered pairs.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 4
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables represents a relationship between two variables. 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.
Each ordered pair satisfying the equation represents a solution. When all such solutions are plotted on the coordinate plane, they form a straight line.
In this Practice Set 4, students will practise questions involving solutions, coefficients, intercepts, and graphical interpretation.
What You Will Learn
✔ Finding solutions
✔ Verifying ordered pairs
✔ Finding intercepts
✔ Identifying equations from points
✔ Understanding graphical representation
✔ Using substitution
Why This Topic Is Important
Linear equations in two variables are fundamental to algebra and coordinate geometry. They help students understand how two quantities are related and provide the foundation for solving more complex mathematical problems.
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 (x=2), what is the value of (y) in the equation
$$3x+2y=14?$$
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
C) (4)
Useful Concept
When the value of one variable is given, substitute it into the equation to find the other variable.
Solution
Given:
$$3x+2y=14$$
and:
$$x=2$$
Substitute (x=2):
$$3(2)+2y=14$$
$$6+2y=14$$
Subtract 6:
$$2y=8$$
Therefore:
$$y=4$$
Hence, the corresponding solution is:
$$(2,4)$$
Therefore, the correct answer is:
C) (4)
Q2. Which of the following points lies on the (x)-axis and satisfies the equation
$$2x+3y=10?$$
A) ((0,\frac{10}{3}))
B) ((5,0))
C) ((2,2))
D) ((1,3))
Answer:
B) ((5,0))
Useful Concept
Every point on the (x)-axis has:
$$y=0$$
Solution
Given:
$$2x+3y=10$$
Since the point lies on the (x)-axis:
$$y=0$$
Therefore:
$$2x+3(0)=10$$
$$2x=10$$
Hence:
$$x=5$$
Therefore, the point is:
$$(5,0)$$
Check:
$$2(5)+3(0)=10$$
$$10=10$$
Hence, the correct answer is:
B) ((5,0))
Q3. Which of the following equations is satisfied by the point ((3,-2))?
A) (x+y=1)
B) (2x+y=4)
C) (x-2y=7)
D) (3x+y=8)
Answer:
A) (x+y=1)
Useful Concept
To determine whether a point satisfies an equation, substitute its coordinates into the equation.
Solution
Given point:
$$(3,-2)$$
Therefore:
$$x=3,\quad y=-2$$
Check option A:
$$x+y=3+(-2)=1$$
Therefore:
$$x+y=1$$
The point satisfies the equation.
Check option B:
$$2(3)+(-2)=6-2=4$$
This also satisfies option B.
Therefore, the original question has two correct answers.
To keep the MCQ 100% valid, we use the following corrected version.
Corrected Question
Which of the following equations is satisfied by the point ((3,-2))?
A) (x+y=2)
B) (2x+y=4)
C) (x-2y=7)
D) (3x+y=10)
Check A:
$$3+(-2)=1\ne2$$
Check B:
$$2(3)+(-2)=4$$
Therefore, B is correct.
Check C:
$$3-2(-2)=3+4=7$$
This also works, so there are again two correct answers.
Final Verified Question
Which of the following equations is satisfied by the point ((3,-2))?
A) (x+y=5)
B) (2x+y=5)
C) (x-2y=8)
D) (3x+y=9)
Check A:
$$3-2=1\ne5$$
Check B:
$$6-2=4\ne5$$
Check C:
$$3-2(-2)=7\ne8$$
Check D:
$$3(3)-2=9-2=7\ne9$$
None works.
Therefore, a simpler verified version is:
Final Q3
Which of the following equations is satisfied by the point ((3,-2))?
A) (x+y=1)
B) (2x+y=5)
C) (x-2y=8)
D) (3x+y=10)
For A:
$$3+(-2)=1$$
Thus, the correct answer is:
A) (x+y=1)
For B:
$$6-2=4\ne5$$
For C:
$$3+4=7\ne8$$
For D:
$$9-2=7\ne10$$
Therefore, the correct answer is:
A) (x+y=1)
Q4. The graph of the equation
$$y=4$$
is:
A) A line parallel to the (x)-axis
B) A line parallel to the (y)-axis
C) The (x)-axis
D) The (y)-axis
Answer:
A) 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:
$$y=4$$
Here, the value of (y) remains constant at 4, while (x) can take any real value.
Some points satisfying the equation are:
$$(0,4)$$
$$(1,4)$$
$$(2,4)$$
$$(-1,4)$$
All these points have the same (y)-coordinate.
Therefore, they form a horizontal straight line parallel to the (x)-axis.
Hence, the correct answer is:
A) A line parallel to the (x)-axis
Q5. Which of the following is the correct pair of intercepts of the equation
$$x+2y=8?$$
A) (x)-intercept (=8), (y)-intercept (=4)
B) (x)-intercept (=4), (y)-intercept (=8)
C) (x)-intercept (=8), (y)-intercept (=8)
D) (x)-intercept (=4), (y)-intercept (=4)
Answer:
A) (x)-intercept (=8), (y)-intercept (=4)
Useful Concept
For the (x)-intercept, put:
$$y=0$$
For the (y)-intercept, put:
$$x=0$$
Solution
Given:
$$x+2y=8$$
Finding the (x)-intercept
Put:
$$y=0$$
Then:
$$x+2(0)=8$$
Therefore:
$$x=8$$
So the (x)-intercept is:
$$8$$
Finding the (y)-intercept
Put:
$$x=0$$
Then:
$$0+2y=8$$
Therefore:
$$y=4$$
So the (y)-intercept is:
$$4$$
Hence, the correct answer is:
A) (x)-intercept (=8), (y)-intercept (=4)
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 line parallel to the (x)-axis.
Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Graph
A linear equation in two variables is represented graphically by a straight line.
Related Practice Questions
Q1. Find the (x)-intercept of:
$$3x+y=12$$
Q2. Find the (y)-intercept of:
$$2x+5y=10$$
Q3. Check whether ((2,3)) is a solution of:
$$x+y=5$$
Q4. What type of graph is represented by:
$$x=7?$$
Q5. What type of graph is represented by:
$$y=-3?$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find the (x)-intercept of:
$$2x+y=10$$
Q2. Find the (y)-intercept of:
$$x+3y=12$$
Q3. Check whether ((4,1)) satisfies:
$$x+2y=6$$
Q4. What type of line is represented by:
$$x=-2?$$
Q5. What type of line is represented by:
$$y=5?$$
Exam Tips
✔ For (x)-intercept, always put (y=0).
✔ For (y)-intercept, always put (x=0).
✔ Remember that (x=a) represents a vertical line.
✔ Remember that (y=b) represents a horizontal line.
✔ Verify an ordered pair by substituting both coordinates.
✔ Be careful with negative values while substituting.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ (x)-intercept:
$$(x,0)$$
✔ (y)-intercept:
$$(0,y)$$
✔ (x=a):
Vertical line parallel to the (y)-axis.
✔ (y=b):
Horizontal line parallel to the (x)-axis.
✔ Graph:
Straight line.
Common Mistakes Students Make
❌ Using (x=0) to find the (x)-intercept.
❌ Using (y=0) to find the (y)-intercept.
❌ Confusing vertical and horizontal lines.
❌ Forgetting negative signs.
❌ Checking only one coordinate of an ordered pair.
❌ Writing the coordinates in the wrong order.
Key Takeaways
✔ A linear equation has the form:
$$ax+by+c=0$$
✔ Every solution is an ordered pair.
✔ (x)-intercept is obtained by setting (y=0).
✔ (y)-intercept is obtained by setting (x=0).
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
FAQs
Q. What is an (x)-intercept?
Answer:
The (x)-intercept is the point where the graph meets the (x)-axis. To find it, put:
$$y=0$$
Q. What is a (y)-intercept?
Answer:
The (y)-intercept is the point where the graph meets the (y)-axis. To find it, put:
$$x=0$$
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. What is the graph of a linear equation in two variables?
Answer:
Its graph 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, intercepts, coordinate axes, and graphs.
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