1.   Which of the following pairs of linear equations has unique solution, no solution, 
or infinitely many solutions. In case there is a unique solution, find it by using cross 
multiplication method.
(i) ${x – 3y – 3 = 0}$                      (ii)  ${2x + y = 5}$
    ${3x – 9y – 2 = 0}$                            ${3x+2y = 8}$

(iii) ${3x – 5y = 20}$                      (iv) ${6x – 10y = 40}$
      ${x – 3y – 7 =0}$                          ${3x – 3y – 15 = 0}$
	  
2. (i)   For which values of a and b does the following pair of linear equations have an infinite 
number of solutions?
		${2x + 3y = 7}$
		${(a – b) x + (a + b) y = 3a + b – 2}$

	(ii) For which value of k will the following pair of linear equations have no solution?
		${3x + y = 1}$
		${(2k – 1) x + (k – 1) y = 2k + 1}$

3. Solve the following pair of linear equations by the substitution and cross-multiplication methods :
		${8x + 5y = 9}$
		${3x + 2y = 4}$

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  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 ₹ 1000 as hostel charges whereas 
	     a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges.
	     Find the fixed charges and the cost of food per day.
	  
	(ii)   A fraction becomes ${1/3}$ when 1 is subtracted from the numerator and it become ${1/4}$
           when 8 is added to its denominator. Find the fraction.
		   
	(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?
		  
     (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 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?
		   
	(v)   The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is 
	      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.