## 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**

**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)**

**SHARMA COACHING CENTRE**

9718041826

Basic-trigonometry-identities

graphing-linear-inequalities solving

Introduction-of-co-ordinate-geometry

probability

materials-metals-and-non-metals

quadratic-equation-word-problems

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)

circle (hindi)

Probability (hindi)

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Mensuration ( Hindi )

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A.P (Hindi)

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Geometry (Hindi)

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Polynomial in hindi

**Read more topics**Basic-trigonometry-identities

graphing-linear-inequalities solving

Introduction-of-co-ordinate-geometry

probability

materials-metals-and-non-metals

quadratic-equation-word-problems

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)

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