NCERT Solutions for Class 9 Maths Chapter 13 — Exercise Set 13.4#
A pair of linear equations in two variables is written as
$$a_1x + b_1y + c_1 = 0, \qquad a_2x + b_2y + c_2 = 0$$Each fact in the situation gives one equation.
Given below are some everyday situations. Construct a pair of linear equations in two variables for each situation.
1. On two different days a family buys movie tickets and snack boxes. Let the cost of one movie ticket be ₹x and the cost of one snack box be ₹y. (i) On the first day, the family buys 2 movie tickets and 3 snack boxes for ₹850. (ii) On the second day, the family buys 4 movie tickets and 1 snack box for ₹1100. #
Solution
On the first day, 2 tickets and 3 snack boxes cost ₹850, so:
$$2x + 3y = 850 \quad \cdots (1)$$On the second day, 4 tickets and 1 snack box cost ₹1100, so:
$$4x + y = 1100 \quad \cdots (2)$$(Solving them gives a ticket price of ₹245 and a snack box price of ₹120.)
2. Two friends, Sahil and Meena, travelled by taxi. Let the fixed charge for one taxi trip be ₹x and the additional charge per kilometre be ₹y. (i) Sahil travelled 6 km and paid a total fare of ₹122. (ii) Meena travelled 8 km and paid a total fare of ₹160. #
Solution
Sahil paid the fixed charge plus 6 km at ₹$y$ per km, ₹122 in all, so:
$$x + 6y = 122 \quad \cdots (1)$$Meena paid the fixed charge plus 8 km, ₹160 in all, so:
$$x + 8y = 160 \quad \cdots (2)$$(Solving them gives a fixed charge of ₹8 and ₹19 per km.)
3. In a sports meet, tickets for adults cost ₹150 each and tickets for children cost ₹100 each. A total of 200 people attended the meet, and the total amount collected from ticket sales was ₹25,000. (Let the number of adult tickets sold be x and the number of children’s tickets sold be y.) #
Solution
200 people attended in all, so:
$$x + y = 200 \quad \cdots (1)$$The ticket money totals ₹25,000, so:
$$150x + 100y = 25000 \quad \cdots (2)$$(Solving them gives 100 adult tickets and 100 children’s tickets.)