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Friday, 26 June 2015

Pair Linear Equations in Two Variables

                                                                                                                   SHARMA SIR 9718041826
 Pair Linear Equations in Two Variables,graph,line,x,y ,solve,age,stream,two digit number,car,speed,

                                     Pair Linear Equations in Two Variables
1. For which values of a and b does the following pair of linear 
equations have an infinite number of solutions? (2 marks)
2x + 2y = 7, (a – b) x + (a + b) y = 3a + b – 2

2. Solve graphically: x + 3y = 6, 2x – 3y =12 (3 marks)

3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month,
the cost of 2 kg of apples and 1kg of grapes is Rs 300. Represent the situation algebraically
and geometrically. (3 marks)

4.find out whether the lines representing the following
pair of linear equation intersect at a point, is parallel or coincident: 
6x – 3y + 10 = 0, 2x – y + 9 = 0. (3 marks)

5. Solve the following pairs of equations: (3 marks)
(i) 4x – 3y – 8 = 0 (ii) 7x + 11y = 3

6. A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km
upstream and 55km down-stream Determine the speed of the stream and that of the boat in
still water. (3 marks)

7. 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? (3 marks)

8. 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 Rs
1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as
hostel charges. Find the fixed charges and the cost of food per day. (3 marks)

9. Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for
each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been
deducted for each incorrect answer, then Yash would have scored 50 marks. How many
questions were there in the test? (3 marks)

10. Places A and B are 100km apart on a highway. One car starts from A and another from B at
the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours.
If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(3 marks)

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