❓ Solve the following pair of linear equations by the elimination method and the substitution
method :
(i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2
(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
<br>
(iv) x/2 + 2y/3 =-1; x-y/3=3
(i) x=19/5, y=6/5<br>
(ii) x = 2, y = 1<br>
(iii) x=9/13, y=-5/13<br>
(iv) x = 2, y = –3
❓ 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
1
2
if we only add 1 to the denominator. What is the fraction?<br>
(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?<br>
(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.<br>
(iv) Meena went to a bank to withdraw ` 2000. She asked the cashier to give her
` 50 and ` 100 notes only. Meena got 25 notes in all. Find how many notes of
` 50 and ` 100 she received.<br>
(v) A lending library has a fixed charge for the first three days and an additional charge
for each day thereafter. Saritha paid ` 27 for a book kept for seven days, while Susy
paid ` 21 for the book she kept for five days. Find the fixed charge and the charge
for each extra day.
2. (i) x – y + 2 = 0, 2x – y – 1 = 0, where x and y are the numerator and denominator of the
fraction;
3
5
× <br>
(ii) x – 3y + 10 = 0, x – 2y – 10 = 0, where x and y are the ages (in years) of Nuri and Sonu
respectively. Age of Nuri (x) = 50, Age of Sonu (y) = 20.<br>
(iii) x + y = 9, 8x – y = 0, where x and y are respectively the tens and units digits of the
number; 18.<br>
(iv) x + 2y = 40, x + y = 25, where x and y are respectively the number of ` 50 and ` 100
notes; x = 10, y = 15.<br>
(v) x + 4y = 27, x + 2y = 21, where x is the fixed charge (in `) and y is the additional
charge (in `) per day; x = 15, y = 3.