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Daily Practice Problems
Class 10 Maths
Pair of Linear Equations in Two Variables
daily practice problem

Question 1:

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

 

Question 2:

Find whether the given pair of linear equations is consistent or inconsistent.

3x + 2y = 8, 6x – 4y = 9

 

Question 3:

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of boat in still water and the speed of stream.

 

Question 4:

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

 

Question 5:

A train covered a certain distance at a uniform speed. If the train would have been 10  faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 ; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

 

Question 6:

The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

 

Question 7:

Find the value of k for which the system kx + 2y = 5 and 3x + y = 1 has

(i) a unique solution                                                   (ii) no solution

 

Question 8:

7x – 5y – 4 = 0 is given. Write another linear equation, so that the lines represented by the pair are:

(i) intersecting                            (ii) coincident                       (iii) parallel

 

Question 9:

Solve the following pair of linear equations:

8x + 5y = 9

3x + 2y = 4

 

Question 10:

Solve:

 +  =

 -  =

 

Question 11:

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then find value of k.

 

Question 12:

Write the number of solutions of the following pair of linear equations:

x + 2y – 8 = 0, 2x + 4y = 16

 

Question 13:

If x = a, y = b is the solution of the pair of equation x – y = 2 and x + y = 4, then find the value of a and b.

 

Question 14:

In ∆ABC, ∠A = x, ∠B = 3x, and ∠C = y if 3y – 5x = 30°, show that triangle is right angled.

 

Question 15:

Half the perimeter of a rectangle garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

 

Question 16:

The solution of  + 3y = 14 and  - 4y = 23 is ______.

 

Question 17:

If a pair of linear equations is consistent, then the lines will be _____.

 

Question 18:

Check whether the pair of equations

x + 3y = 6      

2x – 3y = 12  

is consistent. If so, solve them graphically

 

Question 19:

The graph of x = 2 is a line parallel to ____ axis.

 

Question 20:

How many solutions does the pair of equations y = 0 and y = -5 have?

**********

Problem-solving on Class 10 Maths Pair of Linear Equations in Two Variables NCERT Chapter 3 after learning a theoretical concept is crucial for several reasons:

  1. Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 10 Maths Pair of Linear Equations in Two Variables you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
  2. Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 10 Maths Pair of Linear Equations in Two Variables NCERT Chapter 3, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
  3. Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
  4. Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Pair of Linear Equations in Two Variables Class 10 Maths in practical scenarios helps you remember them better than passive reading or memorization.
  5. Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Pair of Linear Equations in Two Variables Class 10 Maths Notes on LearnoHub.com
  6. Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Pair of Linear Equations in Two Variables. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
  7. Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Pair of Linear Equations in Two Variables Class 10 Maths Online Tests at LearnoHub.com.
  8. Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
  9. Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
  10. Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Pair of Linear Equations in Two Variables Class 10 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 10 Maths Pair of Linear Equations in Two Variables NCERT Chapter 3

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 10 Maths Pair of Linear Equations in Two Variables NCERT Chapter 3 useful.

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  • Class 10 Maths Sample papers