## Lecture-5

CROSS MULTIPLICATION METHOD

00:00:55 NCERT Exercise 3.5 Question 1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (i) x – 3y – 3 = 0 3x – 9y – 2 = 0 (ii) 2x + y = 5 3x + 2y = 8 (iii) 3x – 5y = 20 6x – 10y = 40 (iv) x – 3y – 7 = 0 3x – 3y – 15 = 0

00:13:55 NCERT Exercise 3.5 Question 2 part (i) (i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x + 3y = 7 (a – b) x + (a + b) y = 3a + b – 2

00:21:15 NCERT Exercise 3.5 Question 2 part (ii) (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k – 1) x + (k – 1) y = 2k + 1

00:24:45 NCERT Exercise 3.5 Question 3 Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9 3x + 2y = 4

00:29:15 NCERT Exercise 3.5 Question 4 part (i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.

00:34:25 NCERT Exercise 3.5 Question 4 part (ii) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.