(Q.22). In a garden there are some bees and flowers. If one bee sits on each flower then one bee will be left. If two bees sit on each flower, one flower will be left. Find the number of bees and number of flowers.

Let the number of bees = x and

the number of flowers = y

If one bee sits on each flower then one bee will be left. So, x = + 1

or x - y - = 0 ... (1)

If two bees sit on each flower, one flower will be left. So, x = 2(- 1)

or x - 2y + = 0 ... (2)

For the equation x - y - 1 = 0
x y = x - 1 (x,y)
0 y = - 1 = - (0,-)
1 y = - 1 = (1,)
2 y = - 1 = (2,)
3 y = - 1 = (3,)
4 y = - 1 = (4,)
For the equation x - 2y + 2 = 0
x
y =
x + 2
2
(x,y)
0
y =
+ 2
2
 =
(0,)
2
y =
+ 2
2
 =
(2,)
4
y =
+ 2
2
 =
(4,)
6
y =
+ 2
2
 =
(6,)

In the graph, (, ) is the point of intersection. Therefore, there are bees and flowers