(1) Which of the following pairs of linear equations has unique solution, no solution, infinitely many solutions. In case there is unique solution, find it by using cross multiplication method.

(i)  x – 3y – 3  =  0 and 3x – 9y – 2  =  0      Solution

(ii) 2x + y  =  5 and 3x + 2y  =  8        Solution

(iii) 3x – 5y  =  20 and 6x – 10y  =  40        Solution

(iv) x – 3y – 7  =  0 and 3x – 3y – 15  =  0          Solution

(2) For which values of a and b does the following pair of linear equations have an infinite many solution

2x + 3y  =  7

(a – b)x + (a + b)y  =  3a + b – 2 


(3)   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           Solution

(4) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

(i) A part of monthly hostel charges is fixed and 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 charge and the cost of food per day.           Solution

(ii) A fraction becomes 1/3 when 1 is subtracted from the numerator it becomes 1/4 when 8 is added to its denominator. Find the fraction.            Solution

(iii) 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?          Solution

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car 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?                Solution

(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.


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