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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, ordered pairs, equations, and graphical representation.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 2
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction
Linear Equations in Two Variables is an important chapter in Class 9 Mathematics. A linear equation involving two variables can be expressed in the form:
$$ax+by+c=0$$
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. The collection of all such solutions can be represented graphically by a straight line.
This Practice Set 2 contains 5 fresh MCQs covering solutions, substitution, coefficients, and graphical concepts.
What You Will Learn
✔ Identifying coefficients
✔ Finding values of variables
✔ Checking ordered pairs
✔ Finding solutions of equations
✔ Understanding graphs of linear equations
✔ Intercepts and solutions
✔ Relationship between variables
Why This Topic Is Important
Linear equations in two variables are fundamental to algebra and coordinate geometry. They help students understand relationships between two quantities and prepare them for more advanced mathematical 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. Which of the following ordered pairs is a solution of the equation
$$3x+2y=12?$$
A) ((2,3))
B) ((1,4))
C) ((3,2))
D) ((4,1))
Answer:
A) ((2,3))
Useful Concept
An ordered pair ((x,y)) is a solution if, after substituting the values of (x) and (y), the equation is satisfied.
Solution
Given:
$$3x+2y=12$$
Check option A:
$$x=2,\quad y=3$$
Substituting:
$$3(2)+2(3)$$
$$=6+6$$
$$=12$$
Therefore:
$$3x+2y=12$$
Hence, ((2,3)) is a solution.
Check the other options:
For ((1,4)):
$$3(1)+2(4)=3+8=11\ne12$$
For ((3,2)):
$$3(3)+2(2)=9+4=13\ne12$$
For ((4,1)):
$$3(4)+2(1)=12+2=14\ne12$$
Therefore, the correct answer is:
A) ((2,3))
Q2. If (y=4) is a solution of the equation
$$2x+y=10,$$
then the value of (x) is:
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
A) (3)
Useful Concept
When the value of one variable is given, substitute it into the equation and solve for the other variable.
Solution
Given:
$$2x+y=10$$
and:
$$y=4$$
Substituting (y=4):
$$2x+4=10$$
Subtract 4 from both sides:
$$2x=6$$
Therefore:
$$x=3$$
Hence, the required ordered pair is:
$$(3,4)$$
Therefore, the correct answer is:
B) (3)
Correction: The numerical answer is (3), so the correct option is B, not A.
Q3. The equation
$$5x-3y+7=0$$
has the coefficient of (y) equal to:
A) (5)
B) (-3)
C) (7)
D) (3)
Answer:
B) (-3)
Useful Concept
In the standard form:
$$ax+by+c=0$$
the coefficient of (y) is (b).
Solution
Given:
$$5x-3y+7=0$$
Comparing with:
$$ax+by+c=0$$
we get:
$$a=5$$
$$b=-3$$
$$c=7$$
Therefore, the coefficient of (y) is:
$$-3$$
Hence, the correct answer is:
B) (-3)
Q4. Which of the following is a solution of the equation
$$x-2y=4?$$
A) ((6,1))
B) ((4,2))
C) ((2,-1))
D) ((5,1))
Answer:
A) ((6,1))
Useful Concept
To check an ordered pair, substitute its coordinates into the equation.
Solution
Given:
$$x-2y=4$$
For option A:
$$x=6,\quad y=1$$
Substituting:
$$6-2(1)=6-2=4$$
Therefore, the equation is satisfied.
Now check the other options.
For ((4,2)):
$$4-2(2)=4-4=0\ne4$$
For ((2,-1)):
$$2-2(-1)=2+2=4$$
This also satisfies the equation.
Therefore, option C is also a solution.
This makes the original MCQ invalid because it has two correct answers.
Corrected Question
Which of the following is a solution of:
$$x-2y=5?$$
A) ((7,1))
B) ((4,2))
C) ((2,-1))
D) ((5,1))
Check A:
$$7-2(1)=5$$
Therefore, ((7,1)) is a solution.
Check B:
$$4-2(2)=0\ne5$$
Check C:
$$2-2(-1)=4\ne5$$
Check D:
$$5-2(1)=3\ne5$$
Therefore, the correct answer is:
A) ((7,1))
Q5. Which point lies on the (x)-axis and satisfies the equation
$$x+y=7?$$
A) ((0,7))
B) ((7,0))
C) ((7,7))
D) ((1,7))
Answer:
B) ((7,0))
Useful Concept
Every point on the (x)-axis has:
$$y=0$$
Therefore, to find the point on the (x)-axis, put (y=0) in the equation.
Solution
Given:
$$x+y=7$$
Since the point lies on the (x)-axis:
$$y=0$$
Therefore:
$$x+0=7$$
Hence:
$$x=7$$
So the required point is:
$$(7,0)$$
Check:
$$7+0=7$$
Therefore, the point satisfies the equation.
Hence, the correct answer is:
B) ((7,0))
Important Concepts
Standard Form
A linear equation in two variables is written as:
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Solution
An ordered pair ((x,y)) is a solution if it satisfies the equation.
(x)-Axis
For every point on the (x)-axis:
$$y=0$$
(y)-Axis
For every point on the (y)-axis:
$$x=0$$
Graph
The graph of a linear equation in two variables is a straight line.
Example
For:
$$x+y=7$$
putting (y=0):
$$x=7$$
So:
$$(7,0)$$
lies on the (x)-axis.
Putting (x=0):
$$y=7$$
So:
$$(0,7)$$
lies on the (y)-axis.
Related Practice Questions
Q1. Find the value of (y) when (x=2) in:
$$3x+y=11$$
Q2. Check whether ((4,2)) is a solution of:
$$x+2y=8$$
Q3. Find the coefficient of (x) in:
$$7x-5y+9=0$$
Q4. Find the point where the equation:
$$x+y=10$$
meets the (x)-axis.
Q5. Find the point where:
$$2x+y=6$$
meets the (y)-axis.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which ordered pair satisfies:
$$2x+y=9?$$
A) ((2,5))
B) ((3,3))
C) ((4,1))
D) ((1,6))
Q2. If (x=3) in:
$$x+y=8,$$
find (y).
Q3. What is the coefficient of (y) in:
$$4x-7y+3=0?$$
Q4. Which coordinate is zero for every point on the (y)-axis?
Q5. What is the graph of a linear equation in two variables?
Exam Tips
✔ Always compare an equation with its standard form carefully.
✔ Remember that the sign is included in the coefficient.
✔ To check a solution, substitute both values.
✔ For a point on the (x)-axis, use (y=0).
✔ For a point on the (y)-axis, use (x=0).
✔ Write ordered pairs in the correct order: ((x,y)).
✔ Carefully check arithmetic while substituting values.
Quick Revision Notes
✔ Standard form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
that satisfies the equation.
✔ On (x)-axis:
$$y=0$$
✔ On (y)-axis:
$$x=0$$
✔ Graph of a linear equation:
Straight line
✔ A linear equation in two variables generally has:
Infinitely many solutions
Common Mistakes Students Make
❌ Ignoring the negative sign while identifying a coefficient.
❌ Interchanging (x) and (y) in an ordered pair.
❌ Forgetting to substitute both coordinates.
❌ Assuming (x=0) for a point on the (x)-axis.
❌ Assuming (y=0) for a point on the (y)-axis.
❌ Making calculation errors while solving for the unknown variable.
Key Takeaways
✔ A linear equation in two variables can be written as:
$$ax+by+c=0$$
✔ Its solutions are represented by ordered pairs.
✔ The coefficient includes its algebraic sign.
✔ Every point on the (x)-axis has (y=0).
✔ Every point on the (y)-axis has (x=0).
✔ The graph of a linear equation in two variables is a straight line.
FAQs
Q. What is the standard form of a linear equation in two variables?
Answer:
The standard form is:
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Q. How do we check whether an ordered pair is a solution?
Answer:
Substitute the values of (x) and (y) into the equation. If both sides become equal, the ordered pair is a solution.
Q. What is the value of (y) on the (x)-axis?
Answer:
For every point on the (x)-axis:
$$y=0$$
Q. What is the value of (x) on the (y)-axis?
Answer:
For every point on the (y)-axis:
$$x=0$$
Q. What does the graph of a linear equation in two variables look like?
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, ordered pairs, axes, and basic graphical concepts.
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