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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers based on the latest NCERT syllabus. Learn the substitution method with step-by-step solutions, useful formulas, shortcut tricks, exam tips, and board-level practice questions.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Board Exam Level
Method Covered: Substitution Method (Basic)
Based On: NCERT Latest Syllabus
Introduction:
The substitution method is one of the most commonly used algebraic methods for solving a pair of linear equations in two variables. In this method, one variable is expressed in terms of the other variable from one equation. This expression is then substituted into the second equation to obtain the value of one variable. After finding one variable, its value is substituted back into either equation to determine the other variable.
The substitution method is especially useful when one of the equations is already solved for one variable or can easily be rearranged. It is simple, systematic, and widely used in CBSE Board examinations.
Students should practice this method carefully because it strengthens algebraic manipulation skills and reduces calculation mistakes. In this practice set, the focus is on understanding the basic steps of substitution before solving more advanced questions in later sets.
What You Will Learn?
✔ Meaning of Substitution Method
✔ Steps of Substitution
✔ Solving Linear Equations
✔ Finding the Values of Variables
✔ Verification of Solutions
✔ Board Exam Concepts
Why This Topic Is Important?
The substitution method is one of the three standard algebraic methods prescribed in NCERT and is frequently asked in board examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
————————————————–
Q1. In the substitution method, the first step is:
Question Difficulty:
🟢 Easy
A) Draw the graph
B) Express one variable in terms of the other
C) Multiply both equations
D) Add both equations
Answer:
$$\text{Express one variable in terms of the other}$$
Useful Formula for this Question:
If possible,
$$x=f(y)$$
or
$$y=f(x)$$
Concept Behind This Question:
One equation is rearranged before substitution.
Solution:
In the substitution method, we first isolate one variable.
Example:
$$x=5-y$$
This expression is then substituted into the second equation.
Therefore, the correct answer is:
$$\text{Express one variable in terms of the other}$$
Shortcut / Smart Trick
Choose the equation in which the coefficient of a variable is:
$$1$$
or
$$-1$$
This makes substitution much easier.
Exam Tip:
Always isolate the variable that requires the least calculation.
————————————————–
Q2. Which method is most convenient when one equation is already written as:
$$x=4-y$$
Question Difficulty:
🟢 Easy
A) Graphical Method
B) Elimination Method
C) Substitution Method
D) Cross Multiplication Method
Answer:
$$\text{Substitution Method}$$
Useful Formula for this Question:
Substitute the value directly into the second equation.
Concept Behind This Question:
Already isolated variables reduce calculation.
Solution:
Since
$$x$$
is already expressed in terms of
$$y$$
we simply substitute it into the second equation.
Hence, the most suitable method is:
$$\text{Substitution Method}$$
Shortcut / Smart Trick
Whenever one variable is already isolated, use substitution instead of elimination.
Exam Tip:
Board questions often provide equations that make substitution easier.
————————————————–
Q3. While solving by substitution, after finding one variable, the next step is:
Question Difficulty:
🟢 Easy
A) Stop solving
B) Draw the graph
C) Substitute its value into either equation
D) Multiply both equations
Answer:
$$\text{Substitute its value into either equation}$$
Useful Formula for this Question:
Substitute back after obtaining one variable.
Concept Behind This Question:
Both variables must be determined.
Solution:
Suppose:
$$x=3$$
Substitute
$$x=3$$
into one of the original equations to find
$$y$$
Therefore, the correct answer is:
$$\text{Substitute its value into either equation}$$
Shortcut / Smart Trick
Always substitute into the simpler equation to reduce calculations.
Exam Tip:
Do not forget to calculate both variables.
————————————————–
Q4. The solution of the pair of equations is:
Question Difficulty:
🟡 Medium
A) Only the value of $$x$$
B) Only the value of $$y$$
C) An ordered pair
D) A straight line
Answer:
$$\text{An ordered pair}$$
Useful Formula for this Question:
Solution:
$$(x,\ y)$$
Concept Behind This Question:
Both variables together form the solution.
Solution:
A pair of linear equations has two unknowns.
Hence the final answer is written as:
$$(x,\ y)$$
Therefore, the correct answer is:
$$\text{An ordered pair}$$
Shortcut / Smart Trick
Always write the answer as:
$$(x,\ y)$$
Never write only one variable.
Exam Tip:
Writing only
$$x$$
or
$$y$$
results in an incomplete answer.
————————————————–
Q5. Which of the following ordered pairs satisfies the equations
$$x+y=7$$
and
$$x-y=1$$
Question Difficulty:
🟡 Medium
A) $$(4,\ 3)$$
B) $$(5,\ 2)$$
C) $$(3,\ 4)$$
D) $$(2,\ 5)$$
Answer:
$$(4,\ 3)$$
Useful Formula for this Question:
A solution satisfies both equations simultaneously.
Concept Behind This Question:
Substitute each option into both equations.
Solution:
Check option A.
For
$$(4,\ 3)$$
First equation:
$$4+3=7$$
✔ Correct
Second equation:
$$4-3=1$$
✔ Correct
Therefore,
$$(4,\ 3)$$
satisfies both equations.
Hence, the correct answer is:
$$(4,\ 3)$$
Shortcut / Smart Trick
Instead of solving the equations, verify the options one by one.
This technique is much faster in MCQs.
Exam Tip:
Option verification often saves time in board objective questions.
————————————————–
Important Formulas and Concepts
Standard Form:
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Substitution Steps
Step 1:
Express one variable.
Step 2:
Substitute into the second equation.
Step 3:
Find one variable.
Step 4:
Substitute back.
Step 5:
Write the solution as:
$$(x,\ y)$$
————————————————–
FAQs
Q. When should we use the substitution method?
Answer:
When one variable can easily be isolated.
Q. Is substitution compulsory in board exams?
Answer:
No.
Students may use any correct algebraic method unless the question specifies a particular method.
Q. Can substitution be used for every pair of linear equations?
Answer:
Yes.
However, sometimes elimination or cross multiplication is faster.
————————————————–
Common Mistakes Students Make
❌ Forgetting to substitute back after finding one variable.
❌ Writing only the value of
$$x$$
or
$$y$$
instead of the ordered pair.
❌ Making sign mistakes during substitution.
❌ Rearranging the equation incorrectly.
❌ Forgetting to verify the final answer.
————————————————–
Quick Revision Notes
✔ Isolate one variable first.
✔ Substitute into the second equation.
✔ Find one variable.
✔ Substitute back.
✔ Final answer should be written as:
$$(x,\ y)$$
————————————————–
Conclusion:
These Class 10 Maths Chapter 3 MCQs introduce the substitution method in a simple and systematic manner. Understanding the basic steps of substitution helps students solve linear equations accurately and prepares them for more advanced algebraic methods in upcoming practice sets.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-4
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two variables part-3
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-2
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Part 1
- Class 10 Maths Chapter 2 Polynomials (Graphical Zeroes) – Part 13
- Class 10 Maths Chapter 2 Polynomials graphical representation of polynomials – Part 12
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials ) – Part 11
- Class 10 Maths Chapter 2 Polynomials zeroes of polynomials – Part 10
- Class 10 Maths Chapter 2 Polynomials formation – Part 9
- Class 10 Maths Chapter 2 Forming Quadratic Polynomials – Part 8
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
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