# SCC Education

## Pair Linear Equations in Two Variables

SHARMA SIR 9718041826 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
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)
SHARMA COACHING CENTRE

9718041826

Basic-trigonometry-identities

graphing-linear-inequalities solving

Introduction-of-co-ordinate-geometry

probability

materials-metals-and-non-metals

Trignometry-solved-questions

surface-areas-and-volumes

sequence

linear-equations

Sample paper 1

Sample paper 2

Sample paper 3

Sample paper 4

Circle (Important Question)

Arithmetic Progression

circle (hindi)

Probability  (hindi)

### Polynomial in hindi 