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Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Let 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 per day charge is 3 Rs.

Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

Let the number of Rs 50 notes be x and 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.

Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Let the unit digit of the number be x and 10's digit be y. Now, According to the question, 24323 Also Now adding (1) and (2) we get, now putting this value in (1) Hence the number is 18.  

Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Let the age of Nuri be x and 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 age of Nuri is 20.

Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes \frac{1}{2 } if we only add 1 to the denominator. What is the fraction?

Let the numerator of the fraction be x and 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  .

Q1.    Solve the following pair of linear equations by the elimination method and the substitution method :

                (iv)    \frac{x}{2} + \frac{2y}{3} = -1\ \textup{and} \ x - \frac{y}{3} = 3

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,

Q1.    Solve the following pair of linear equations by the elimination method and the substitution method :

                    (iii)    3x - 5y -4 = 0\ \textup{and} \ 9x = 2y + 7

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,

Q1.    Solve the following pair of linear equations by the elimination method and the substitution method :

                    (ii)    3x + 4 y = 10 \ \textup{and} \ 2x - 2y = 2

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,

Q1.    Solve the following pair of linear equations by the elimination method and the substitution method :

                    (i)    x + y =5 \ \textup{and} \ 2x - 3y = 4

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,
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