default_background

Find the best tutors and institutes for Class 10 Tuition

Find Best Class 10 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Q1(iii):
Solve the following pair of linear equations by the substitution method. (iii) 3x – y = 3; 9x – 3y = 9

Solution :

Given: A pair of linear equations in two variables:

(1) $3x - y = 3$

(2) $9x - 3y = 9$

To Find: The solution $(x, y)$ for the given pair of linear equations using the substitution method.

Step 1: Express one variable in terms of the other using Equation (1).

From Equation (1):

$3x - y = 3$

Add $y$ to both sides:

$3x = 3 + y$

Subtract $3$ from both sides:

$y = 3x - 3$ --- (Equation 3)

Step 2: Substitute the expression for $y$ into Equation (2).

Equation (2) is $9x - 3y = 9$.

Substitute $y = 3x - 3$ into Equation (2):

$9x - 3(3x - 3) = 9$

Step 3: Solve the resulting equation.

Distribute the $-3$ across the terms inside the parentheses:

$9x - 9x + 9 = 9$

Combine the $x$ terms ($9x - 9x = 0$):

$0 + 9 = 9$

$9 = 9$

Step 4: Interpret the result.

[Since the variable $x$ has been eliminated and we have arrived at a true statement ($9 = 9$), this indicates that the two equations are dependent and represent the same line.]

Specifically, if we divide Equation (2) by $3$:

$\frac{9x}{3} - \frac{3y}{3} = \frac{9}{3}$

$3x - y = 3$

This is identical to Equation (1). Therefore, the pair of linear equations has infinitely many solutions.

Step 5: General form of the solution.

Since the equations are coincident, any value of $x$ will yield a corresponding value of $y$ that satisfies both equations. We can express the solution set as:

$y = 3x - 3$ for any real number $x$.

Final Answer: The pair of linear equations has infinitely many solutions, represented by the relation $y = 3x - 3$.


More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2


CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable


Chapters in CBSE - Class 10 Mathematics


Top Tutors who teach Pair of linear equations in two variable

(5)
Top Tutor
locationImg Mahipalpur, Delhi
experience 14 yrs of Exp
I'm professional tutor, teaching maths for last 14 years. Maximizing potential of student through.
homeTutions Student's Home

As an experienced teacher for nine years, I have been teaching to make students interested in the subjects of Maths. My attitude is to help children improve in studies in the best possible way.

Skills: Mathematics
Also teaches: Class 11 Tuition, Class 9 Tuition and more

(19)
Top Tutor
locationImg Ashok Vihar, Delhi
experience 10 yrs of Exp students 2 students
greenClock 121 hrs of classes completed
rsIcon 380 per hour
My students are my strength
Online Classes Online Classes
homeTutions Student's Home

Being a professional tutor , I have an experience of more than 9 years , my students are my strength , i always dedicated for my students.

Aditya Bajaj

A+ tutor for Maths and Science class 10. Highly recommended, very humble and polite. You should go for him without doubts.

Skills: English , Mathematics and more
Also teaches: UPSC Exams Coaching, Class 6 Tuition and more

(10)
Top Tutor
locationImg Nigdi, Pune
experience 6 yrs of Exp
greenClock 1 hrs of classes completed
rsIcon 400 per hour
Junior Scientist in Biomedical Field
Online Classes Online Classes
homeTutions Student's Home

I have excellent teaching experience of 7 years with best results with my previous student's from CBSE , STATE and ICSE BOARD'S . Preferably i focus on students personal interest, level of understanding and study methodology. I am here to give best of me to seek best out from my students. I have given seminar on 'Students changing Virtue towards study , Need if time??' . Passionate to guide students towards there destiny

Skills: Mathematics , Physics and more
Also teaches: Class 11 Tuition, Class 12 Tuition and more

(48)
superTutorSuper Tutor
locationImg Kodambakkam, Chennai
experience 15 yrs of Exp students 57 students
greenClock 4039 hrs of classes completed
rsIcon 800 per hour
Maths and Science for 10th std. Score 💯
Online Classes Online Classes

With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.

Devanath Bharadwaj

Shri Seshadri sir was able to break the jinx of my son not learning indefinitely, with his experience in smoothly sliding into a routine with such interactive, yet nonchalant transition for my son's education. Thankyou sir, thankyou UrbanPro.

Skills: Mathematics , Physics and more
Also teaches: UPSC Exams Coaching, Class 8 Tuition and more

(177)
Top Tutor
locationImg Purasaiwakkam Otteri, Chennai
experience 10 yrs of Exp students 36 students
greenClock 3569 hrs of classes completed
rsIcon 200 per hour
15 Years of Experience in teaching Spoken English & Academic subjects for Class IX-XII
Online Classes Online Classes

I have a total of 10 years of teaching experience. I am Teaching Online for Overseas and Local Students. My Students are from INDIA, UK, USA, INDONESIA & THAILAND. My passion is Teaching. I am Focusing on CBSE, IGCSE, IB, ICSE,&NIOS,.I have conducted National level conference and workshop, Hands-on-training, Seminar, etc Teaching with Human touch produces a great result. My students of class 10th had proven with good results.

Skills: Mathematics , Social Science and more
Also teaches: Nursery-KG Tuition, Class 11 Tuition and more

Find more Tutor for Pair of linear equations in two variable in your City


Other Subjects in CBSE - Class 10

Worksheet Icon

Download free CBSE - Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »