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Learn Solution of linear equations

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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superTutorSuper Tutor
locationImg Nangli, Amritsar
15 yrs of Exp 12 students
greenClock 2474 hrs of classes completed
rsIcon 400 per hour
CBSE/ICSE Maths & Physics Expert (8–10) | Top 100 Tutors 2025 | 15 Yrs Exp | 5⭐ by 50+ Students
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I can teach Maths and Physics Few of my students have become Aircraft Engineer, Automobile Engineer, Lieutenants, I feel proud of. In the pursuit of cracking exams like IIT JEE CUET etc many a time students forget to solidify their basics but just go for speed. That is a mistake First, under the beauty of all fundamental concepts then go for time management

Mihira Sulakhe

It has been a week now and my daughter has started liking her Class 9 Maths tuition. Earlier she would dread going to other Maths tuitions. So I am a happy parent. Onkar sir is passionate about teaching and it shows. The classes are interactive, with a small batch of 5 students, focus on fundamentals, and at the same time engaging and interesting for the students.

Skills: Mathematics , Physics and more
Also teaches: Class 10 Tuition, Math Olympiad and more

Akshay Aggarwal Class 9 Tuition trainer in Delhi
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superTutorSuper Tutor
locationImg Badarpur, Delhi
10 yrs of Exp 67 students
greenClock 3745 hrs of classes completed
rsIcon 200 per hour
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I am an experienced tutor with nine years of teaching under my belt. I hold a BSc degree in geography. My passion for teaching has always been my driving force. I take pride in the fact that I have helped many of my students to score well on their exams and achieve their academic goals. I have provided home tuition to students of grades sixth to tenth in maths, science, and social studies for nine years. I cater to CBSE board students only, except for chemistry, where I also take up ICSE and IB board. My classes are conducted online and offline, and I allocate one hour daily to each student. I follow the CBSE teaching pattern and ensure the NCERT syllabus is covered. My approach towards teaching is student-centric, where I focus on their individual needs and pace of learning. I understand that not all students have the same learning capabilities, so I ensure each student receives personalised attention. To make the learning experience more engaging and interactive, I use animations and PPTs in my classes. The notes and tests I provide are designed to help the students understand the concepts thoroughly. Learning should not be a mundane task but an enjoyable experience. I aim to make the learning process more fun and exciting for my students so that they can develop a love for learning.

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I enrolled my son for grade 9 math practice. And sir has really helped him understand the concepts he could never understand before. His confidence has grown and I have noticed remarkable improvement in his math skills. Sir is really patient and skilled.

Skills: Mathematics , Chemistry and more
Also teaches: Class 11 Tuition, Class 8 Tuition and more

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locationImg Sector 78, Noida
5 yrs of Exp 2 students
greenClock 45 hrs of classes completed
rsIcon 300 per hour
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I am a passionate tutor providing online and offline tuitions for mathematics, science, and social studies. My students have achieved scores ranging from 93 to 95. My main motto is not only to increase the marks of the student but also to improve the knowledge in the subject. 

Skills: Mathematics , Social Science and more

Sai V. Class 9 Tuition trainer in Madappanahalli
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locationImg Itagalpura Main Rd, Madappanahalli
17 yrs of Exp 45 students
greenClock 3602 hrs of classes completed
rsIcon 400 per hour
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: Class 11 Tuition, Class 10 Tuition and more

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locationImg Sarai Jullena, Delhi
4 yrs of Exp 5 students
greenClock 200 hrs of classes completed
rsIcon 300 per hour
Experienced instructor with 5 years of experience in Teaching Mathematics and Science
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I have been teaching class 9, class 10 since 2014. I have taught students from DPS Faridabad, HKH Public School Ajmer, Govt Boys School Delhi etc. Till now i have taught 5 students of class 9, 3 students of class 10 and 4 students from elementary classes. I teach science and math very logically for clear understanding of topics. I give students practical examples related with real life for visualizing the application areas and their leaning becomes a fun when i tell theories behind concepts. I have structured notes, class test and revision schedule well in advance so that students get best practice and understanding their subjects wisely before final exam. My experience shows that students are taking interest in learning at this class so they need proper guidance and direction in studies. i support my students in achieving their academic goals and also guide them as a mentor.

Skills: Mathematics , Science

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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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