Question

Form the pair of linear equations in the following problems, and find their solutions graphically.

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

Answer 1

Let the cost of 1 pencil be Rs x and the cost of 1 pen be Rs y.

According to the question, the algebraic representation is

5x + 7y = 50

7x + 5y = 46

For 5x + 7y = 50,

x = `(50 - 7y)/5`

x	3	10	-4
y	5	0	10

7x + 5y = 46

x = `(46-5y)/7`

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines intersect each other at point (3, 5). Therefore, the cost of a pencil and a pen are Rs 3 and Rs 5 respectively.