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.

Q2(ii):
Write four solutions for each of the following equations: (ii) $\pi x + y = 9$

Solution :

Initial Setup & Algebraic Formulation

We are tasked with finding four distinct solutions for the following linear equation in two variables:

$\pi x + y = 9$

A linear equation in two variables has infinitely many solutions. A solution is defined as an ordered pair $(x, y)$ that satisfies the equation. To systematically generate these solutions, we will express one variable in terms of the other.

Step 1: Isolating the Dependent Variable

To make the calculation of ordered pairs straightforward, we isolate the dependent variable ($y$) in terms of the independent variable ($x$). [Per the Subtraction Property of Equality, subtracting $\pi x$ from both sides of the equation yields:]

$y = 9 - \pi x$

We can now substitute arbitrary real numbers for $x$ to compute the corresponding exact values of $y$.

Step 2: Deriving the First Solution

Let us assign $x = 0$. Substituting this value into our isolated equation:

$y = 9 - \pi(0)$

$y = 9 - 0$

$y = 9$

Thus, the first solution is the ordered pair $(0, 9)$. [This point also represents the y-intercept of the linear graph].

Step 3: Deriving the Second Solution

Let us assign $x = 1$. Substituting this value into the equation:

$y = 9 - \pi(1)$

$y = 9 - \pi$

Thus, the second solution is the ordered pair $(1, 9 - \pi)$.

Step 4: Deriving the Third Solution

Let us assign $x = 2$. Substituting this value into the equation:

$y = 9 - \pi(2)$

$y = 9 - 2\pi$

Thus, the third solution is the ordered pair $(2, 9 - 2\pi)$.

Step 5: Deriving the Fourth Solution

Let us assign $x = -1$. Substituting this value into the equation:

$y = 9 - \pi(-1)$

$y = 9 + \pi$

Thus, the fourth solution is the ordered pair $(-1, 9 + \pi)$.

Step 6: Tabular Summary of Solutions

We can organize the derived solutions into a Cartesian coordinate table. This demonstrates the linear relationship and prepares the data for graphical representation.

Independent Variable ($x$) Dependent Variable ($y$) Ordered Pair $(x, y)$
$0$ $9$ $(0, 9)$
$1$ $9 - \pi$ $(1, 9 - \pi)$
$2$ $9 - 2\pi$ $(2, 9 - 2\pi)$
$-1$ $9 + \pi$ $(-1, 9 + \pi)$

Step 7: Graphical Representation of the Linear Equation

Below is the geometric interpretation of the equation $\pi x + y = 9$ plotted on a Cartesian plane. The line represents the locus of all infinite solutions, with our four specific calculated points highlighted. (Note: For spatial plotting purposes, $\pi$ is approximated as $3.14$).

x y 0 1 2 -1 9 (0, 9) (1, 9-π) (2, 9-2π) (-1, 9+π) πx + y = 9

Final Solution: Four valid solutions for the equation $\pi x + y = 9$ are $(0, 9)$, $(1, 9 - \pi)$, $(2, 9 - 2\pi)$, and $(-1, 9 + \pi)$.


More Questions from Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.2


CBSE Solutions for Class 9 Mathematics Linear Equations in Two Variables


Chapters in CBSE - Class 9 Mathematics


Top Tutors who teach Linear Equations in Two Variables

(14)
Top Tutor
locationImg Jawahar Nagar Sector 5, Jaipur
experience 4 yrs of Exp students 1 student
greenClock 20 hrs of classes completed
rsIcon 350 per hour
It Professional Trainee With 4years of Experience
Online Classes Online Classes
regularClasses Tutor's home

As a dedicated and experienced educator, I offer personalized class 6 to 10 and till BCA in a supportive online learning environment. With a strong background in Mathematics, Science, and Computers, I am committed to helping students achieve academic excellence and develop a deep understanding of complex concepts. My teaching approach is centered around clarity, simplicity, and innovative methods, ensuring that students of all learning styles feel engaged and motivated. With a proven track record of consistently high academic achievement and a passion for inspiring a love for learning, I am confident in my ability to make a positive impact on my students' academic journeys.

Skills: English , Mathematics and more
Also teaches: BCA Tuition, Career Counselling and more

(37)
Top Tutor
locationImg Ashok Nagar D' Souza Layout, Bangalore
experience 6 yrs of Exp students 13 students
greenClock 818 hrs of classes completed
rsIcon 400 per hour
Learn and grow with Statistician having 10 years of experience in teaching and Government projects.
Online Classes Online Classes

I am a teacher , a statistician and a data analyst. I am willing to give online tution to uh in subject maths and statistics. I am a first ranker in my university in MSc (Statistics) and a gold medalist. I am certified in O level. I have cleared written exam for the post statistical officer in 2022 conducted by UPSC. Also cleared exam of MES but could not make in the interview. My key skills are teaching, solving queries, understanding students, visualising and analysing data. I have 6 years experience in teaching and i was a junior consultant having 4 years of experience in Ministry of labour and employment,Shimla . Currently i am working as a Monitoring Assistant in Department of Fisheries, Ministry of Fisheries,Animal Husbandry and Dairying, New Delhi. I know languages like R, python etc.

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

(15)
Top Tutor
locationImg Ashok Nagar D' Souza Layout, Bangalore
experience 7 yrs of Exp students 9 students
greenClock 198 hrs of classes completed
rsIcon 300 per hour
Guiding Minds, Shaping Futures, Inspiring
Online Classes Online Classes

I am an experienced , qualified with experience of 5 years , across different boards including CBSE, ICSE, IGCSE and State Board. Passionate about teaching, over the years I have helped thousands of students .

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

(48)
superTutorSuper Tutor
locationImg Kodambakkam, Chennai
experience 15 yrs of Exp students 57 students
greenClock 3953 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

(26)
Top Tutor
locationImg Serlingampally, Hyderabad
experience 20 yrs of Exp students 13 students
greenClock 623 hrs of classes completed
rsIcon 400 per hour
TEACHING IS MY PASSION-I STILL STRIVE TO BETTER MY TEACHING ABILITIES
Online Classes Online Classes
regularClasses Tutor's home

Teaching is my Passion. I have taught Mathematics, Physics and Chemistry to several students during 20+ years of my teaching. Many of my students who initially were scarred of Mathematics, have developed interest on the subject and opted MPC group in their Intermediate and are now earning Dollars as Software Engineers in USA, CANADA, UK and Australia.

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

Find more Tutor for Linear Equations in Two Variables in your City


Other Subjects in CBSE - Class 9

Worksheet Icon

Download free CBSE - Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.2 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »