Find the best tutors and institutes for Class 10 Tuition
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.
Solution :
Given:
1. The difference between two numbers is $26$.
2. One number is three times the other number.
To Find:
The two numbers.
Step 1: Defining the Variables
Let the larger number be $x$.
Let the smaller number be $y$.
Step 2: Formulating the Linear Equations
Based on the given conditions, we can form the following system of linear equations:
Equation (1): $x - y = 26$ [Since the difference between the two numbers is 26]
Equation (2): $x = 3y$ [Since one number is three times the other]
Step 3: Applying the Substitution Method
The substitution method involves substituting the value of one variable from one equation into the other equation.
We already have $x$ expressed in terms of $y$ in Equation (2): $x = 3y$.
Substitute $x = 3y$ into Equation (1):
$(3y) - y = 26$
Step 4: Solving for $y$
Simplify the expression:
$2y = 26$
Divide both sides by $2$:
$y = \frac{26}{2}$
$y = 13$
Step 5: Solving for $x$
Now, substitute the value of $y = 13$ back into Equation (2) to find $x$:
$x = 3y$
$x = 3(13)$
$x = 39$
Step 6: Verification
Check the results against the original conditions:
Difference: $39 - 13 = 26$ (Condition 1 satisfied)
Ratio: $39 = 3 \times 13$ (Condition 2 satisfied)
Final Answer: The two numbers are 39 and 13.
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(iii): Solve the following pair of linear equations by the substitution method. (iii) 3x – y = 3; 9x – 3y = 9
- 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(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
Top Tutor
Chinsurah R S, Hooghly
15 yrs of
Exp
7 students
987 hrs of classes completed
350
per hour
Online Classes
Tutor's home
I've taught at least 150 students of this Class till date ....online/offline together.
Very good teacher and friendly also. I have already join this sir's class. Very helpful teacher definitely. Thank you so much for your support. Highly recommended to all. Has good grip in the concept.
Top Tutor
Ashok Vihar, Delhi
10 yrs of
Exp
2 students
121 hrs of classes completed
380
per hour
Online Classes
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.
A+ tutor for Maths and Science class 10. Highly recommended, very humble and polite. You should go for him without doubts.
Top Tutor
Asilmetta, Visakhapatnam
3 yrs of
Exp
Online Classes
Student's Home
Tutor's home
Seeing my students succeed is the best reward! I bring lessons to life with real-world examples, and I put my all into every class. It's amazing to watch them not only understand the material but also get excited about learning. Their good grades are definitely a confidence booster!
Top Tutor
Sector 31 31C, Chandigarh
7 yrs of
Exp
28 students
Online Classes
Student's Home
Tutor's home
I have been teaching for seven years. . I am teaching maths for cbse, icse,IB (international baccalaureate)' usa and uk (precalculus, AP calculus, algebra) acdamic students up to 12 grade and students preparing for SAT, OLYMPIAD, engineering and IIT ENTRANCE . Besides this I am also teaching Physics and Chemistry. I love teaching. I have excellent communication skills, a good understanding of concepts, ability to motivate students. Since every student has a different understanding level so for me its essential to know in what way students will understand and to explain them quickly. I also like to help in teaching someone who is financially weak to get an education. I can assure you to give 100% results. I will give you free demo classes and Pay me only when you will be completely satisfied with my teaching. I am btech from IIT Delhi Now I am full time in teaching
Indirapuram, Ghaziabad
8 yrs of
Exp
3 students
300
per hour
Online Classes
Student's Home
I am a teacher of maths and science, having a experience of 8+ years in teaching, done my schooling from CBSe board and degree from IP university.
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
