Question-1 :-  Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

  Let us denote age of Aftab x and age of his daughter y. 
  Then the algebraic representation is given by the following equations:

  x – 7 = 7 (y – 7)
  x - 7 = 7y - 49 
  x - 7y = -49 + 7
  x - 7y = -42  .......(i)
  
  x + 3 = 3 (y + 3) 
  x + 3 = 3y + 9  
  x - 3y = 9 - 3  
  x - 3y = 6 ......(ii)

  Lets represent these equations in graphically: 
  x - 7y = -42  .......(i)

    

        
x
0
7
    
    

        
y
6
7
    

  x - 3y = 6 ......(ii)

    

        
x
0
6
    
    

        
y
-2
0
    

  Plot the points A(0, 6), B(-42, 0) and P(0, -2), Q(6, 0), corresponding to the solutions in Table.
  Now draw the lines AB and PQ, representing the equations x - 7y = -42  and x - 3y = 6, as shown in following Figure:

    

Question-2 :-  The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Represent this situation algebraically and geometrically.

  Let x and y be the bats and balls.
  3x + 6y = 3900 
   x + 2y = 1300 .......(i)

   x + 2y = 1300 ........(ii)
  
  Lets represent these equations in graphically: 
  x + 2y = 1300 .......(i)

    

        
x
0
1300
    
    

        
y
650
0
    

  x + 2y = 1300 ........(ii)

    

        
x
0
1300
    
    

        
y
650
0
    

  Plot the points A(0, 650), B(1300, 0) and P(0, 650), Q(1300, 0), corresponding to the solutions in Table.
  Now draw the lines AB and PQ, representing the equations x + 2y = 1300 and x + 2y = 1300, as shown in following Figure:

  But, this is the same as Equation (i). 
  Hence the lines represented by Equations (i) and (ii) are coincident. 
  Therefore, Equations (i) and (ii) have infinitely many solutions. 
    

Question-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 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and geometrically.

  Let us denote apples by x and grapes by y. 
  The algebraic representation is given by the following equations:

  2x + y = 160  ...........(i) 

  4x + 2y = 300  
  2x + y = 150...........(ii)
  
  Lets represent these equations in graphically: 
  2x + y = 160  ...........(i) 

    

        
x
50
60
    
    

        
y
60
40
    

  2x + y = 150...........(ii)

    

        
x
70
75
    
    

        
y
10
0
    

  Plot the points A(0, 160), B(80, 0) and P(0, 150), Q(75, 0), corresponding to the solutions in Table.
  Now draw the lines AB and PQ, representing the equations 2x + y = 160 and 2x + y = 150, as shown in following Figure: