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There are various methods for solving the linear equation. In the previous exercises graphical method and one of the algebraic methods for solving the equation have been discussed. There are many algebraic methods for solving equations, like substitution and elimination methods. Similar to the substitution method elimination method is also used to solve the linear equation. In this method, multiply the equation by numbers to make the coefficient of the equation equal. This will help to eliminate the value and get the solution.
These class 10 maths exercise 3.3 solutions are designed as per the students' demand, covering comprehensive, step-by-step solutions of every problem. Practice is necessary for all these questions to command the concepts, boost confidence and in-depth understanding of concepts. In the exercise, all the NCERT solutions are covered according to the syllabus of the NCERT. These solutions help the students to understand the concept in depth. This exercise included all the questions given in the NCERT Books. In exercise 3.3 of the NCERT, the chapter solutions are explained in detail.
Q1(i) Solve the following pair of linear equations by the elimination method and the substitution method :
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we get
Now, adding (2) and (3), we get
Substituting this value in (1), we get
Hence,
Substitution method :
Given, equations
Now, from (1) we have,
Substituting this value in (2)
Substituting this value of x in (3)
Hence,
Q1(ii) Solve the following pair of linear equations by the elimination method and the substitution method :
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2 we get
Now, adding (1) and (3), we get
Putting this value in (2) we get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
Substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we get
Now, subtracting (3) from (2), we get
Putting this value in (1), we get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
Substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2, we get
Now, adding (1) and (3), we get
Putting this value in (2), we get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
Substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Let the numerator of the fraction be x, and the denominator is y,
Now, according to the question,
Also,
Now, subtracting (1) from (2), we get
Putting this value in (1)
Hence,
And the fraction is:
Answer:
Let the age of Nuri be x and the age of Sonu be y.
Now, according to the question
Also,
Now, subtracting (1) from (2), we get
Putting this value in (2)
Hence, the age of Nuri is 50 and the age of Nuri is 20.
Answer:
Let the unit digit of the number be x and the 10's digit be y.
Now, according to the question,
Also
Now adding (1) and (2), we get,
Now putting this value in (1)
Hence, the number is 18.
Answer:
Let the number of Rs 50 notes be x and the number of Rs 100 notes be y.
Now, according to the question,
And
Now, subtracting (1) from (2), we get
Putting this value in (1).
Hence, Meena received 10, 50 Rs notes and 15, 100 Rs notes.
Answer:
Let the fixed charge be x, and per day charge is y.
Now, according to the question,
And
Now, Subtracting (2) from (1). We get,
Putting this in (1)
Hence, the fixed charge is 15 Rs and the per-day charge is 3 Rs.
Also Read:
Also see-
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Graphical Method
Elimination method
Elimination method as it is time-efficient and not lengthy.
We multiply both the equations with some non-zero constant to eliminate one of the variables by adding both of the new equations.
In order to make the coefficient of one of the variables numerically equal but with opposite signs so that they get cancelled when we add them together.
Yes, once we find the value of the first variable, we substitute its value in any of the equation to get the value of the second equation.
It doesn’t provide us the desired point if the values are irrational.
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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