5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.
Question:

5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.

Solution:

Given:

(i) 5 pens and 6 pencils together cost of Rs. 9.

(ii) 3 pens and 2 pencils cost Rs. 5.

To Find: Cost of 1 pen and 1 pencil.

Let

(i) The cost of 1 pen = Rs x.

(ii) The cost of 1 pencil = Rs y.

According to question

$5 x+6 y=9$$\ldots \ldots(1) 3 x+2 y=5$$\ldots \ldots(2)$

Thus we get the following system of linear equation

$5 x+6 y-9=0$…(3) from eq. 1

$3 x+2 y-5=0$..(4) from eq. 2

By using cross multiplication we have

$\frac{-x}{(-30)-(-18)}=\frac{-y}{(-25)-(-27)}=\frac{1}{(10)-(18)}$

$\frac{x}{-30+18}=\frac{-y}{-25+27}=\frac{1}{10-18}$

$\frac{x}{-12}=\frac{-y}{2}=\frac{1}{-8}$

$\therefore \quad x=\frac{-12}{-8}$

$x=\frac{12}{8}$

$=\frac{3}{2}$

$x=\frac{3}{2}$

$\therefore y=\frac{2}{8}$

$y=\frac{1}{4}$

Cost of one pen $=$ Rs. $\frac{3}{2}$

Cost of one pencil $=$ Rs. $\frac{1}{4}$