Question

5 pens and 6 pencils together cost Rs. 9.00 .and 3 pens and 2 pencils cost Rs.5.00 . find the cost of 1 pen and 1 pencil. 

Answer 1

Let cost of one pen = x
   cost of one pencil = y

5 pens and 6 pencils cost Rs. 9
⇒ 5x + 6y = 9  ....................(1)
⇒ 5x = 9 - 6y
⇒ x = (9-6y)/5
3 pens and 2 pencils cost Rs 5
⇒3x + 2y = 5

⇒3($\frac{9-6y}{5}$) + 2y = 5

⇒$\frac{27}{5} - \frac{18y}{5} +2y = 5$

⇒$27 -18y +10y = 5*5$

⇒$27 -8y = 25$

⇒ $-8y = 25-27 =-2 \\ y =(-2)/(-8) = 0.25$

x = $(9-6y)/5 = (9-6(1/4))/5 = 7.5/5 = 1.5$

Cost of one pen = Rs. 1.5
Cost of one Pencil = Rs. 0.25
So cost of one pen and one pencil = 1.5+0.25 = Rs 1.75

Answer 2

Let the cost of pen be x and pencil be y,
ATQ
5x+6y=9                                                               ...(i)
and  
3x+2y-=5                                                             ...(ii)
solving (i) and (ii) by eliminatory method we get;
    5x+6y=9
    3x+2y=5( Multiply by 3)
-> 9x+6y=15       ...(iii)
From (i) and (iii)
   5x  +  6y=   9
   9x  +  6y=  15 
(-)     (-)       (-)
------------------------
   4x            =  6
------------------------
or x= 1.5
Substituting the value of x in (ii) we get
3(1.5)+ 2y=5
->4.5+2y=5
->2y= 5-4.5
-> y=0.5/2
->y=0.25 

Therefore cost of pen is Rs1.5 and that of pencil is Rs0.25.