Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs Quiz
Are you confused by the different methods for solving Chapter 3, ‘Pair of Linear Equations in Two Variables’? Do techniques like the Substitution and Elimination Methods seem challenging?
Don’t worry! We have the perfect resource to help you: the Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs Quiz. This free online test will help you practice all the important concepts of this chapter and understand them with ease. Let’s strengthen your board exam preparation with this comprehensive Linear Equations quiz!
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Pair of Linear Equations in Two Variables MCQs Quiz
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Q1: The general form of a pair of linear equations in two variables is:
Explanation: The general form of a pair of linear equations in two variables is written as two equations: \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) where \( a_1, b_1, c_1, a_2, b_2, c_2 \) are real numbers and \( a_1^2 + b_1^2 \neq 0, a_2^2 + b_2^2 \neq 0 \).
Q2: Which of the following pairs of equations is NOT a pair of linear equations in two variables?
A: \( 2x + 3y = 7; 4x + 6y = 14 \)
B: \( 3x^2 + 2y = 5; x + y = 3 \)
C: \( x + 2y = 6; 2x – 3y = 4 \)
D: \( 5x + 4y = 8; 10x + 8y = 16 \)
Explanation: A linear equation has the degree of each variable as 1. In option B, the first equation \( 3x^2 + 2y = 5 \) has x with degree 2, so it is not linear. All other options have both equations linear (maximum degree of variables is 1).
Q3: What will be the graphical representation of the pair of linear equations \( x + y = 5 \) and \( 2x + 2y = 10 \)?
A: Coincident lines
B: Intersecting lines
C: Parallel lines
D: None
Explanation: The given equations are: \( x + y = 5 \) and \( 2x + 2y = 10 \) Dividing the second equation by 2: \( x + y = 5 \) Both equations are the same, so their graphs will be the same line lying on top of each other (coincident lines). Such a pair has infinitely many solutions.
Q4: What is the nature of the solution of the pair of linear equations \( 3x + 2y = 5 \) and \( 2x – 3y = 7 \)?
A: No solution
B: Infinitely many solutions
C: A unique solution
D: Two solutions
Explanation: For a pair of linear equations \( a_1x + b_1y = c_1 \) and \( a_2x + b_2y = c_2 \): If \( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \), then there is a unique solution. Here, \( \frac{a_1}{a_2} = \frac{3}{2} \) and \( \frac{b_1}{b_2} = \frac{2}{-3} = -\frac{2}{3} \) Since \( \frac{3}{2} \neq -\frac{2}{3} \), there is a unique solution.
Q5: Solve the following pair of equations by substitution method: \( x + y = 14 \) and \( x – y = 4 \)
A: x=8, y=6
B: x=9, y=5
C: x=10, y=4
D: x=7, y=7
Explanation: Substitution method: From the first equation: \( x = 14 – y \) …(1) Substitute this into the second equation: \( (14 – y) – y = 4 \) \( 14 – 2y = 4 \) \( -2y = 4 – 14 = -10 \) \( y = 5 \) Put the value of y in (1): \( x = 14 – 5 = 9 \) Thus, solution: x=9, y=5
Q6: Solve the following pair of equations by elimination method: \( 3x + 4y = 10 \) and \( 2x – 2y = 2 \)
A: x=2, y=1
B: x=1, y=2
C: x=3, y=0.5
D: x=0, y=2.5
Explanation: Elimination method: Equations: \( 3x + 4y = 10 \) …(1) \( 2x – 2y = 2 \) or \( x – y = 1 \) …(2) [dividing by 2] Multiply (2) by 4: \( 4x – 4y = 4 \) …(3) Add (1) and (3): \( (3x+4y) + (4x-4y) = 10+4 \) \( 7x = 14 \) ⇒ \( x = 2 \) Put x in (2): \( 2 – y = 1 \) ⇒ \( y = 1 \) Thus, solution: x=2, y=1
Q7: The number of solutions of the pair of linear equations \( 2x + 3y = 8 \) and \( 4x + 6y = 7 \) is:
A: A unique solution
B: Two solutions
C: Infinitely many solutions
D: No solution
Explanation: Condition: If \( \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \), then there is no solution (inconsistent). Here, \( \frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2} \), \( \frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2} \), \( \frac{c_1}{c_2} = \frac{8}{7} \) Since \( \frac{1}{2} \neq \frac{8}{7} \), there is no solution. Graphically, these are two parallel lines.
Q8: If the graphs of a pair of linear equations are intersecting lines, then the number of solutions is:
A: No solution
B: Infinitely many solutions
C: A unique solution
D: Two solutions
Explanation: The graphs of a pair of linear equations can be of three types: 1. Intersecting lines → A unique solution (point of intersection) 2. Coincident lines → Infinitely many solutions 3. Parallel lines → No solution Thus, for intersecting lines, there is a unique solution.
Q9: On solving the pair of equations \( 0.2x + 0.3y = 1.3 \) and \( 0.4x + 0.5y = 2.3 \), the values of x and y are:
A: x=1, y=3
B: x=2, y=3
C: x=3, y=2
D: x=4, y=1
Explanation: By elimination method: First equation: \( 0.2x + 0.3y = 1.3 \) …(1) Second equation: \( 0.4x + 0.5y = 2.3 \) …(2) Multiply (1) by 2: \( 0.4x + 0.6y = 2.6 \) …(3) Subtract (2) from (3): \( (0.4x+0.6y) – (0.4x+0.5y) = 2.6 – 2.3 \) \( 0.1y = 0.3 \) ⇒ \( y = 3 \) Put y in (1): \( 0.2x + 0.3(3) = 1.3 \) \( 0.2x + 0.9 = 1.3 \) ⇒ \( 0.2x = 0.4 \) ⇒ \( x = 2 \) Thus, solution: x=2, y=3
Q10: If \( x = 3, y = 4 \) is a solution of the equation \( 3x – 2y = k \), then the value of k is:
A: 1
B: 2
C: 3
D: 4
Explanation: Substituting x=3 and y=4 in the equation \( 3x – 2y = k \): \( 3(3) – 2(4) = k \) \( 9 – 8 = k \) \( k = 1 \) Thus, the value of k is 1.
Q11: The solutions of the pair of linear equations \( 5x – 3y = 11 \) and \( -10x + 6y = -22 \) are:
A: A unique solution
B: No solution
C: Infinitely many solutions
D: Two solutions
Explanation: Condition: If \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \), then there are infinitely many solutions (consistent). Here, \( \frac{5}{-10} = -\frac{1}{2} \), \( \frac{-3}{6} = -\frac{1}{2} \), \( \frac{11}{-22} = -\frac{1}{2} \) Since all three ratios are equal, there are infinitely many solutions. The second equation is -2 times the first, so both equations are equivalent.
Q12: By substitution method, the solution of the pair of equations \( 2x + 3y = 9 \) and \( 3x + 4y = 5 \) is:
A: x=21, y=15
B: x=-21, y=17
C: x=21, y=-17
D: x=-21, y=-17
Explanation: Substitution method: First equation: \( 2x + 3y = 9 \) ⇒ \( 3y = 9 – 2x \) ⇒ \( y = \frac{9 – 2x}{3} \) …(1) Substitute in the second equation: \( 3x + 4\left(\frac{9 – 2x}{3}\right) = 5 \) \( 3x + \frac{36 – 8x}{3} = 5 \) Multiply both sides by 3: \( 9x + 36 – 8x = 15 \) \( x + 36 = 15 \) ⇒ \( x = 15 – 36 = -21 \) Put x in (1): \( y = \frac{9 – 2(-21)}{3} = \frac{9 + 42}{3} = \frac{51}{3} = 17 \) Thus, solution: x=-21, y=17
Q13: The first step in the elimination method is:
A: To find the value of one variable in terms of the other
B: To graph the equations
C: To add both equations
D: To make the coefficients of one variable equal (or opposite) in both equations
Explanation: In the elimination method, we first make the coefficients of one variable equal (or opposite) so that the variable can be eliminated. For this, we multiply the equations by suitable numbers. Then we add or subtract the equations so that one variable is eliminated.
Q14: For the pair of equations \( \frac{x}{2} + \frac{y}{3} = 2 \) and \( \frac{x}{4} + \frac{y}{6} = 1 \), choose the correct statement:
A: Coincident lines, infinitely many solutions
B: Intersecting lines, unique solution
C: Parallel lines, no solution
D: None
Explanation: First equation: \( \frac{x}{2} + \frac{y}{3} = 2 \) ⇒ multiply by 6: \( 3x + 2y = 12 \) Second equation: \( \frac{x}{4} + \frac{y}{6} = 1 \) ⇒ multiply by 12: \( 3x + 2y = 12 \) Both equations are the same, so they are coincident lines and have infinitely many solutions.
Q15: On drawing the graph of the pair of linear equations \( x + 2y = 5 \) and \( 3x + 6y = 15 \), we get:
A: Two intersecting lines
B: The same line
C: Two parallel lines
D: None
Explanation: Dividing the second equation \( 3x + 6y = 15 \) by 3 gives \( x + 2y = 5 \), which is the same as the first equation. Thus, both equations represent the same line. On the graph, it will be the same line (coincident lines).
Quiz Results
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Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs Quiz
Chapter 3, ‘Pair of Linear Equations in Two Variables,’ teaches you various methods to solve two linear equations simultaneously. In this chapter, you will learn how to solve a pair of linear equations using the Graphical Method, Substitution Method, Elimination Method, and Cross-Multiplication Method. You will also understand when a pair of equations is Consistent (having a unique or infinite solution), Inconsistent (having no solution), or Dependent. Understanding the nature of the solution based on the graphs of the lines is a key skill tested in the CBSE Class 10 Maths Quiz and board exams.
Conclusion
Mastering the ‘Pair of Linear Equations in Two Variables’ chapter is crucial for scoring well, and it requires proficiency in various solving methods. Our Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs Quiz is designed to help you achieve this proficiency. This quiz gives you repeated practice on key techniques like the Substitution Method and Elimination Method, enabling you to choose the correct method quickly during an exam. By solving these objective questions, you can improve your speed and accuracy, gaining the confidence to score full marks in this chapter. Start this Free Online Maths Quiz for Class 10 now!
FAQs on Class 10 Maths Chapter 3
1. Question: How many marks from the chapter Pair of Linear Equations are asked in the board exam? Answer: This chapter typically carries 8-10 marks in the CBSE board exam, including MCQs, short answer, and long answer questions.
2. Question: What are the most important methods for solving this chapter? Answer: All methods are important, but the Substitution Method and Elimination Method are frequently asked in exams.
3. Question: Is this Linear Equations quiz based on the NCERT syllabus? Answer: Yes, our Pair of Linear Equations in Two Variables Class 10 quiz is completely based on the NCERT curriculum and the CBSE syllabus.
4. Question: What is the difference between consistent and inconsistent equations? Answer: Consistent equations have at least one solution (lines intersect at a point or are coincident), while inconsistent equations have no solution (lines are parallel).
5. Question: Is this online quiz free? Answer: Yes, this Free Online Maths Quiz for Class 10 is completely free for you to practice anytime, anywhere.
6. Question: How should I prepare this chapter for the board exam? Answer: First, understand all the solving methods clearly and practice questions on each. Then, solve the examples and exercises from the NCERT book. Finally, test your skills with our Linear Equations Online Test.
7. Question: What does the graphical method of solution represent? Answer: In the graphical method, both equations are plotted on a graph. If the lines intersect at a point, it represents a unique solution. If they are coincident, there are infinite solutions. If they are parallel, there is no solution.
8. Question: When is the cross-multiplication method useful? Answer: The cross-multiplication method is very useful when the coefficients of the equations are complex, making other methods more cumbersome.
9. Question: Does this quiz include word problems? Answer: Yes, this quiz includes questions that involve converting real-life problems into a pair of linear equations and then solving them.
10. Question: What is the benefit of taking this online quiz? Answer: This quiz helps you improve time management, learn to select the correct method quickly, and understand the exam pattern, which boosts your confidence for better performance.
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