Question

Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) $10$ students of Class X took part in a Mathematics quiz. If the number of girls is $4$ more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) $5$ 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

i) Consider number of boys $=x$

and number of girls $=y.$

According to the question,

$x+y=10$
or, $y=10-x$ ………(i)
$y=x+4$ ………..(ii)

$x+y=10$:- $\begin{array}{ccccc}x& 1& 2& 3& 4\\ y& 9& 8& 7& 6\end{array}$

$y=x+4$:- $\begin{array}{ccccc}x& 1& 2& 3& 4\\ y& 5& 6& 7& 8\end{array}$

Graphical solution : Girls $=7,$ boys $=3$

(ii) Consider price of a pencil is $x$

and price of a pen is $y.$

According to the question,

$5x+7y=50$.....(i)
$7x+5y=46$ .….(ii)

$7x+5y=46$:- $\begin{array}{ccccc}x& 1& 2& 3& 4\\ y& 7.8& 6.4& 5& 4.2\end{array}$

$5x+7y=50$:- $\begin{array}{ccccc}x& 1& 2& 3& 4\\ y& 6.4& 5.7& 5& 4.2\end{array}$

Graphical solution :

Price of a pencil is Rs $3$

Price of a pen is Rs $5.$