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Equations Reducible to a Pair of Linear Equations in Two Variables

2 pencils and...

Question

2 pencils and 3 pens together costs Rs.33 and 2 pens and 3 pencils together costs Rs. 27. What is the cost of one pencil and one pen?

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Solution

Case 1

Let the cost of the pencil be- x

Let the cost of the pen be- y

Total cost- Rs.33

(Eq. 1.) 2x+3y=33

Case 2

Total cost= Rs.27

(Eq. 2.) 3x+2y=27

Therefore, from eq. 1 and 2,

2x+3y=33

3x+2y=27

By using elimination method

Multiply eq. 1 from 3 and eq. 2 from 2

6x+9y=99………. (Eq. 3)

6x+4y=54……….(Eq. 4)

By solving eq. 3 and 4, we get,

5y=45

y=9

By substituting the value of y in eq. 1

2x+3*9=33

2x+27=33

2x=6

x=3

Therefore, x=3 and y=9

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