5 pencils and 7 pens together cost Rs 50, whereas . . .

Question : 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

Doubt by Ziya

Text Solution : 

Let the cost of 1 pencil = Rs x

and the cost of 1 pen = Rs y

ATQ
5x+7y=50 — (1)

7x+5y=46 — (2)

Using equation (1)

5x+7y=50
5x=50-7y
x=[50-7y]/5 

⭐ Putting y=0
x=[50-7(0)]/5
x=50/5
x=10
(10,0)

⭐ Putting y=10

x=[50-7(10)]/5
x=[50-70]/5
x=-20/5
x=-4

(-4,10)

⭐ Putting y=5

x=[50-7(5)]/5
x=[50-35]/5
x=15/5
x=3

(3,5)

x	10	-4	3
y	0	10	5

Using Equation (2)

7x+5y=46 
5y=46-7x
y=[46-7x]/5

⭐ Putting x=8
y=[46-7(8)]/5
y=[46-56]/5
y=-10/5
y=-2

(8,-2)

⭐ Putting x=-2
y=[46-7(-2)]/5
y=[46+14]/5
y=60/5
y=12

(-2,12)

⭐ Putting x=-12
y=[46-7(-12)]/5
y=[46+84]/5
y=130/5
y=26

(-12,26)

x	8	-2	-12
y	-2	12	26

Plot both the equations on the graph paper by using the gap of 2 on both x and y axes.

Both the graph will intersect each other at (3,5)
Hence, (3,5) is the solution of both the equations. 

x=3
y=5

Hence, 
The cost of 1 Pencil = Rs 3
and the cost of 1 Pen = Rs 5

Video Solution :