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Learn Solution of linear equations

Solving Linear Equations Step-by-Step video thumbnail

Solving Linear Equations Step-by-Step

In CBSE Class 9 Mathematics, the chapter on Linear Equations in Two Variables introduces you to algebraic relationships that represent real-world situations with two unknown quantities. Imagine you have ₹100 to spend on notebooks and pens; the number of notebooks and pens you can buy will vary, but their total cost remains fixed. This scenario can be expressed as a mathematical equation. A linear equation in two variables is written in the standard form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Finding a "solution" to this equation means discovering the specific pairs of values for the two variables that perfectly satisfy the condition.

The core logic behind the solution of linear equations lies in finding an ordered pair (x, y) that makes the left-hand side (LHS) of the equation equal to the right-hand side (RHS). Unlike linear equations in one variable, which have a single unique solution, a linear equation in two variables has infinitely many solutions. To calculate these solutions mathematically, you simply choose any random value for one variable (say, x), substitute it into the equation, and solve for the corresponding value of the other variable (y). Because you can pick an infinite number of values for x, you will continuously generate an infinite number of corresponding y values, creating an endless list of valid (x, y) coordinate pairs.

Solutions of a Linear Equation: x + y = 5 Algebraic Method Step 1: Let x = 0 0 + y = 5 → y = 5 → Solution: (0, 5) Step 2: Let x = 2 2 + y = 5 → y = 3 → Solution: (2, 3) Step 3: Let y = 0 x + 0 = 5 → x = 5 → Solution: (5, 0) x y (x,y) 0 5 (0, 5) 2 3 (2, 3) 5 0 (5, 0) Graphical Method X Y O 1 2 3 4 5 6 1 2 3 4 5 6 (0, 5) (2, 3) (5, 0) x + y = 5

The diagram above illustrates both the algebraic and graphical approaches to finding the solutions of the linear equation x + y = 5. On the left, we use the substitution method to create a table of values. By picking random numbers for x (like 0, 2, and 5), we calculate the corresponding y values (5, 3, and 0), giving us the ordered pairs (0, 5), (2, 3), and (5, 0). On the right, these exact pairs are plotted on a Cartesian plane. When connected, these coordinate points form a perfectly straight line. In your school exams, you will frequently be asked to plot these lines; the golden rule to remember here is that every single point that lies on this straight line is a valid solution to the equation, beautifully proving why linear equations in two variables have an infinite number of solutions.

Mastering graphical plots, coordinate geometry, and algebraic expressions can sometimes feel challenging, but personalized guidance can make these concepts crystal clear. If you are struggling with CBSE Class 9 Mathematics or simply want to score top marks in Linear Equations in Two Variables, consider connecting with a highly experienced tutor. On the UrbanPro platform, you can easily find verified, expert Mathematics tutors offering both interactive online tuition and localized offline tuition tailored specifically to your learning pace and syllabus needs. Search on UrbanPro today to build a strong mathematical foundation for your board exams!


Other Concepts in Linear Equations in Two Variables


Other Concept Videos for Solution of linear equations

Solving Linear Equations Step-by-Step video thumbnail

Solving Linear Equations Step-by-Step

CBSE - Class 9>Mathematics>Linear Equations in Two Variables>Solution of linear equations


Solving Linear Equations Step-by-Step video thumbnail

Solving Linear Equations Step-by-Step

CBSE - Class 9>Mathematics>Linear Equations in Two Variables>Solution of linear equations

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locationImg Sector 92, Gurgaon
20 yrs of Exp 20 students
greenClock 1281 hrs of classes completed
rsIcon 800 per hour
Teaching mathematics since last 20 years. Doing research on Vedic mathematics
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Teaching since last 20 years

Nandini Mishra

Amit ji is a fantastic teacher. My daughter is very happy with her studies. He is exactly what she needed, a teacher with deep understanding of his subject and a very good communicator. If there is one gripe that I may mention, it's time. We would love to have more classes to cover Physics, but he is completely booked for his time. I would highly recommend him. Thank you.

Skills: Mathematics , Physics and more
Also teaches: Class 11 Tuition, Soft Skills Training and more

Avishake Chatterjee Class 9 Tuition trainer in Kolkata
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8 yrs of Exp 7 students
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rsIcon 700 per hour
MATHS EXPERT having an experience of 6+years
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As a passionate mathematics teacher, I have always enjoyed imparting knowledge to others. I am a B.Tech graduate in Electronics and Communication. I have been teaching mathematics for over four years, and my love for the subject has grown stronger with time. I started teaching as a part-time tutor while pursuing my engineering degree and fell in love with the profession. After completing my degree, I worked with Byjus, one of the leading Edtech companies in India, as a mathematics teacher for two years. While I enjoyed my time at Byju's, I could do more as a teacher and wanted to explore new avenues. I joined Vedantu, an online learning platform, where I have been teaching mathematics for the last two years. I started my journey as a math teacher out of pure passion. Mathematics has always been my favourite subject, and I enjoyed solving problems and equations from a young age. As I grew older, I realised I had a natural talent for teaching, and I decided to pursue it as a career. Currently, I provide mathematics classes for students from sixth to twelfth for all boards, including ICSE, CBSE, and West Bengal. I teach offline and online classes, each lasting for one and a half hours. I use interactive tools such as Zoom, Pentab, and One Note to make my lessons engaging and interactive for my students. To help my students excel in mathematics, I provide them with reference books, notes, and in-built assignments to test their knowledge. I also conduct monthly tests to assess their progress and identify improvement areas. Teaching on UrbanPro has allowed me to interact with students from different parts of the country and help them realise their full potential in mathematics. I want to continue making a positive impact in the lives of my students and help them develop a love for mathematics, just like I did

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Avishake Sir is an exceptional maths teacher! Engaging, patient, and effective. He break down complex concepts into easy-to-understand bits , provide individual attention and boost confidence. Highly recommended!"

Skills: Mathematics
Also teaches: Class 7 Tuition, Class 6 Tuition and more

Sai V. Class 9 Tuition trainer in Madappanahalli
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17 yrs of Exp 43 students
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MSc, BEd , (Phd), Member of Royal Society UK
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I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classes IX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.

Skills: Mathematics , Physics and more
Also teaches: Engineering Entrance Coaching, Parenting and more

(59)
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locationImg Sector 5, Dwarka, Delhi
10 yrs of Exp 33 students
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10 Yrs in Teaching, Conduct Batch Of Two Kids, One-to-One classes. ShortTermPrep & LongTermClasses.
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I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). Works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. ------------------------------------------------------------------------------- Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have one to one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. ------------------------------------------------------------------------------- I took classes and batches in different institutions.

Surabhi rai

The teacher is very good. He understands the students strength and weakness and decides the pace of learning. He also tries to make the student comfortable and at ease with his/her capacity and then works on the child. It is not just Math he works on but the child's confidence and comfort with the subject. Highly recommended.

Skills: Mathematics , Physics and more
Also teaches: Spoken English, Python Training and more

(26)
superTutorSuper Tutor
locationImg Rohini Sector-24, Delhi
20 yrs of Exp 10 students
greenClock 1404 hrs of classes completed
rsIcon 450 per hour
Experienced Maths teacher with more than 20 years of experience.
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I am a teacher and I have been teaching for the past 20 years. l am presently teaching in a school. l have done MSc in Maths and have taught many students.

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Skills: Mathematics , Physics and more
Also teaches: Class 8 Tuition, Class 12 Tuition and more

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Other Subjects in CBSE - Class 9


FAQ

What is the meaning of Solution of linear equations?

It refers to a specific mathematical method or property in Linear Equations in Two Variables used to solve problems involving Solution of linear equations.

Why is Solution of linear equations important for CBSE - Class 9 exams?

This concept is crucial for the exams as questions related to Linear Equations in Two Variables and specifically Solution of linear equations are very common. It helps secure marks in the section effectively.

Is Solution of linear equations part of the latest NCERT syllabus?

Yes, Solution of linear equations is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Linear Equations in Two Variables chapter.

What are common mistakes students make with Solution of linear equations?

Students often miss the minute details or fundamental definitions of Solution of linear equations. Regular revision and practice are needed to master the nuances.

How should I approach learning Solution of linear equations?

Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.

How can UrbanPro help me understand Solution of linear equations better?

UrbanPro connects you with experienced Mathematics tutors who can explain Solution of linear equations with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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