Find the best tutors and institutes for Class 10 Tuition
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
- Q1(i): Solve the following pair of linear equations by the substitution method. (i) x + y = 14; x – y = 4
- Q1(ii): Solve the following pair of linear equations by the substitution method. (ii) s – t = 3; $\frac{s}{3} + \frac{t}{2} = 6$
- Q1(iv): Solve the following pair of linear equations by the substitution method. (iv) 0.2x + 0.3y = 1.3; 0.4x + 0.5y = 2.3
- Q1(v): Solve the following pair of linear equations by the substitution method. (v) $\sqrt{2}x + \sqrt{3}y = 0$; $\sqrt{3}x - \sqrt{8}y = 0$
- Q1(vi): Solve the following pair of linear equations by the substitution method. (vi) $\frac{3x}{2} - \frac{5y}{3} = -2$; $\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
- Q2: Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘$m$’ for which y = mx + 3.
- Q3(i): Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is 26 and one number is three times the other. Find them.
- Q3(ii): Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Q3(iii): Form the pair of linear equations for the following problems and find their solution by substitution method. (iii) The coach of a cricket team buys 7 bats and 6 balls for ` 3800. Later, she buys 3 bats and 5 balls for ` 1750. Find the cost of each bat and each ball.
- Q3(iv): Form the pair of linear equations for the following problems and find their solution by substitution method. (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ` 105 and for a journey of 15 km, the charge paid is ` 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- Q3(v): Form the pair of linear equations for the following problems and find their solution by substitution method. (v) A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
- Q3(vi): Form the pair of linear equations for the following problems and find their solution by substitution method. (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
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
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.
Being a professional tutor , I have an experience of more than 9 years , my students are my strength , i always dedicated for my students.
A+ tutor for Maths and Science class 10. Highly recommended, very humble and polite. You should go for him without doubts.
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
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.
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.
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.
Find more Tutor for Pair of linear equations in two variable in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2 worksheets
Download Now