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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. Solve unique MCQs on graphical representation, elimination, substitution, consistency of equations, and applications with detailed solutions for CBSE and state board exams.
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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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
The chapter Pair of Linear Equations in Two Variables teaches students how to solve two equations containing two unknowns using different mathematical techniques. Students also understand the graphical interpretation of equations and identify whether a system has a unique solution, no solution, or infinitely many solutions. This chapter is highly important for board examinations and competitive tests.
What You Will Learn?
✔ Graphical Interpretation
✔ Elimination Method
✔ Substitution Method
✔ Cross Multiplication Method
✔ Consistency of Linear Equations
✔ Word Problems
✔ Board Exam Based Concepts
Why This Topic Is Important?
Linear equations are widely used in Mathematics and real-life situations involving age, distance, money, and business calculations. This chapter improves logical thinking and is one of the most frequently tested topics in Class 10 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. The solution of the equations
$$2x+y=7$$
$$x+y=5$$
is:
A)
$$(2,3)$$
B)
$$(3,2)$$
C)
$$(4,1)$$
D)
$$(1,4)$$
Answer:
$$(2,3)$$
Useful Formula for this Question:
Subtract one equation from the other to eliminate a variable.
Solution:
Given,
$$2x+y=7$$
$$x+y=5$$
Subtracting,
$$x=2$$
Substitute into
$$x+y=5$$
$$2+y=5$$
$$y=3$$
Hence, the correct answer is:
$$(2,3)$$
Q2. If the graphs of two equations coincide, then the equations are said to be:
A) Inconsistent
B) Independent
C) Dependent
D) Parallel
Answer:
Dependent
Useful Formula for this Question:
Coincident lines satisfy
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
Solution:
When two equations represent the same line, every point on one line also lies on the other.
Therefore, the equations are dependent and have infinitely many solutions.
Hence, the correct answer is:
Dependent
Q3. Which method is based on making the coefficients of one variable equal?
A) Graphical Method
B) Elimination Method
C) Substitution Method
D) Trial Method
Answer:
Elimination Method
Useful Formula for this Question:
Multiply the equations so that one variable has equal coefficients before adding or subtracting.
Solution:
In the elimination method, suitable multiplication is done so that one variable is removed after addition or subtraction.
Hence, the correct answer is:
Elimination Method
Q4. If
$$5x-2y=16$$
and
$$x=4$$
then the value of
$$y$$
is:
A)
$$1$$
B)
$$2$$
C)
$$3$$
D)
$$4$$
Answer:
$$2$$
Useful Formula for this Question:
Substitute the known value into the equation.
Solution:
Given,
$$5x-2y=16$$
Substitute
$$x=4$$
$$20-2y=16$$
$$2y=4$$
$$y=2$$
Hence, the correct answer is:
$$2$$
Q5. Which of the following is a pair of linear equations in two variables?
A)
$$x^2+y=5$$
B)
$$x+y=8,\quad 2x-y=1$$
C)
$$xy=6$$
D)
$$y=\frac{1}{x}$$
Answer:
$$x+y=8,\quad 2x-y=1$$
Useful Formula for this Question:
A linear equation contains variables of degree one only.
Solution:
A pair of linear equations must contain only first-degree variables.
Among the given options,
$$x+y=8$$
and
$$2x-y=1$$
are both linear equations.
Hence, the correct answer is:
$$x+y=8,\quad 2x-y=1$$
Important Formulas and Concepts
Standard Form
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Condition for Unique Solution
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
Condition for No Solution
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Condition for Infinitely Many Solutions
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
Methods of Solving
✔ Graphical Method
✔ Elimination Method
✔ Substitution Method
✔ Cross Multiplication Method
FAQs
Q. What is meant by dependent equations?
Answer:
Dependent equations represent the same straight line and have infinitely many solutions.
Q. Which method removes one variable directly?
Answer:
The elimination method removes one variable by adding or subtracting suitable equations.
Q. What is a linear equation?
Answer:
A linear equation is an equation in which the highest power of every variable is 1.
Common Mistakes Students Make
❌ Forgetting that linear equations have variables of degree one only.
❌ Making sign errors while subtracting equations.
❌ Using incorrect ratios when checking consistency.
❌ Confusing dependent equations with inconsistent equations.
❌ Incorrect substitution after finding one variable.
Quick Revision Notes
✔ Linear equations contain variables with power 1 only.
✔ Dependent equations have infinitely many solutions.
✔ Elimination method removes one variable.
✔ Graphical method uses straight lines.
✔ Check consistency using the ratios of coefficients.
✔ Practice solving equations using more than one method for better understanding.
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions – are based on the latest NCERT syllabus and include completely new, non-repeated questions. Regular practice of these board-oriented MCQs strengthens conceptual understanding, improves calculation speed, and helps students perform confidently in CBSE board exams, state board exams, school tests, and scholarship examinations.
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