Class 10 Maths
Pair of Linear Equations in Two Variables
Solution of Linear equation in 2 variables
There are two approaches for solve linear equation in 2 variables
- Graphical Approach
- Algebraic Approach
Graphical Approach: Draw the graph of both equations
- If lines intersect at a single point, the it has a unique solution
- If lines are parallel, then equations have no solution
- If lines are coincident, then equations have infinitely many solutions.
Case 1 Example: (Unique Solution) Sum of boys & girls in a class is 3. Boys are more than girls by 1. Find number of boys & girls.
Let number of Boys be x, & number of girls be y. then as per questions, we can form a pair of liner equation in two variables: x+y =3 & x-y =1.
Any two Solution for x+y=3 are (3,0) & (0,3). Plot these points & join them to form Green line.
Any two Solution for x-y=1 are (1,0) & (2,1). Plot these points & join them to form Blue line
These 2 lines intersect at (2,1), thus x=2 & y=1 is unique solution for this case.
Case 2 Example: (No Solution):Let’s find solution for x + 2y – 4 = 0 & 2x + 4y – 12 = 0
Any two Solution for x+2y-4=0 are (0,2) & (4,2). Plot these points & join them to form Green line.
Any two Solution for 2x+4y=12 are (0,3) & (6,0). Plot these points & join them to form Blue line.
Notice that these lines are parallel & thus there is no solution for this pair of linear equation.
Case 3 Example: (Infinite Solution): x+y=3 & 2x+ 2y =6.
Let’s plot these equations on the graph.
Any two Solution for x +y =3 are (3,0) & (0,3). Plot these points & join them to form Green line.
Any two Solution for 2x +2y = 6 are (3,0) & (0,3). Plot these points & join them to form Blue line.
Notice that these tow lines Coincide & thus have many solutions.
A pair of linear equations which has no solution, is called an inconsistent pair of linear equations.
A pair of linear equations in two variables, which has a solution, is called a consistent pair of linear equations.
A pair of linear equations which are equivalent has infinitely many distinct common solutions. Such a pair is called a dependent pair of linear equations in two variables. Note that a dependent pair of linear equations is always consistent
Class 10 Maths Pair of Linear Equations in Two Variables NCERT Chapter 3 Free Notes for Best Revision
Revision of Class 10 Maths Pair of Linear Equations in Two Variables is a crucial aspect of effective learning. Revision plays a vital role in the learning process and is especially important before exams. Here are some key points you can consider emphasizing in your content:
- Retention and Memory: Regularly reviewing and revisiting the material of Class 10 Maths Pair of Linear Equations in Two Variables helps reinforce the concepts in students' minds. It strengthens memory pathways, making it easier to recall information during exams and beyond.
- Consolidation of Knowledge: When you revise notes, you are essentially consolidating your knowledge. This means connecting new information with what you already know, making the overall understanding more robust.
- Identifying Knowledge Gaps: Revision allows students to identify any gaps in their understanding or areas where they need further clarification. This gives you a chance to seek help or delve deeper into those topics. For detailed understanding, you can always refer to the videos of Pair of Linear Equations in Two Variables Class 10 Maths NCERT Chapter 3 on LearnoHub.com
- Building Confidence: As you revise Pair of Linear Equations in Two Variables Class 10 Maths and become more familiar with the content, your confidence in your abilities grows. Confidence is a crucial factor in exam performance as it reduces anxiety and allows you to approach exams with a positive mindset.
- Different Revision Techniques: Use a variety of revision techniques such as summarizing notes, creating flashcards, practicing past papers, discussing concepts with peers, and teaching others. Different techniques work for different students, and it's essential to find what suits you the best. You can also attend the LIVE Revision classes on LearnoHub.com or watch the LIVE Revision Race videos of LearnoHub on Pair of Linear Equations in Two Variables Class 10 Maths NCERT Chapter 3.
- Spacing Effect: Spacing out revision sessions over time, rather than cramming all at once, has been shown to improve long-term retention. Create a revision schedule leading up to the exams to allow for spaced practice.
- Regular Revision over Cramming: Regular and consistent revision throughout the academic year is very important. Waiting until the last moment to cram everything can be overwhelming and less effective than spaced-out revision.
- Self-Assessment: Assess your understanding periodically through quizzes or self-tests. This helps you to gauge your progress and identify areas that need further attention. Refer Class 10 Pair of Linear Equations in Two Variables Online Tests.
- Balanced Approach: Remind students to strike a balance between revision and other activities. Adequate rest, exercise, and relaxation are essential for optimal learning and performance.
- Seeking Help: If you face difficulties during the revision process, Refer the videos of Class 10 Maths Pair of Linear Equations in Two Variables. Clearing doubts promptly is crucial for a better grasp of the subject matter. You can always ask your doubts on Pair of Linear Equations in Two Variables Class 10 Maths NCERT Chapter 3. “Ask a Question” section of LearnoHub.com
By highlighting the benefits and strategies of effective revision, you can approach your studies more mindfully and achieve better results in your exams. Best of luck bachhon!
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Always remember, it is very important to study with full concentration during Revision. Here are a few tips for you on how to revise with full focus:
- Create a Distraction-Free Environment: Find a quiet and comfortable place to study where you can minimize distractions. Turn off or silence your phone, log out of social media accounts, and inform others around you that you need uninterrupted study time. A dedicated study environment will help you focus better.
- Set Specific Goals: Before starting your study session, set clear and achievable goals. Break down your study material into smaller tasks, and plan what you want to accomplish during each session. Having specific goals will give you a sense of direction and purpose, making it easier to concentrate.
- Use the Pomodoro Technique: The Pomodoro Technique is a time management method that involves studying in short, focused intervals, typically 25 minutes, followed by a short break of 5 minutes. After completing four sessions, take a longer break of around 15-30 minutes. This technique can improve focus and productivity by providing regular breaks to recharge.
- Stay Organized: Keep your study materials, notes, and resources well-organized. Having everything you need at hand will save time and reduce distractions caused by searching for materials. Use color-coded folders or digital tools to maintain a structured study system.
- Practice Mindfulness and Meditation: Before you begin studying, take a few minutes to practice mindfulness or meditation. Deep breathing exercises and clearing your mind of distractions can help you approach your study session with a calm and focused mindset.
Remember, studying with full concentration is a skill that takes time and practice to develop. If you find your mind wandering during study sessions, gently bring your focus back to the task at hand and be patient with yourself. With consistent effort, you can improve your ability to concentrate and make the most of your study time.
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