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 Rs50, whereas 7 pencils and 5 pens together cost Rs46. Find the cost of one pencil and that of one pen.

Answer 1

(i) Let the number of girls be $x$ and the number of boys be $y.$

According to the question, the algebraic representation is $x + y = 10 x − y = 4$ For $x + y = 10, x = 10 − y;$

$x$	$5$	$4$	$6$
$y$	$5$	$6$	$4$

For $x − y = 4, x = 4 + y$

$x$	$5$	$4$	$3$
$y$	$1$	$0$	$-1$

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines intersect each other at points $(7, 3)$.

Therefore, the number of girls and boys in the class is $7$ and $3$ respectively.

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(ii) 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 $5x + 7y = 50,$
$x= 50-\dfrac{7y}{5}$

$x$	$3$	$10$	$-4$
$y$	$5$	$0$	$10$

$7x + 5y = 46$
$x= 46-\dfrac{5y}{7}$

$x$	$8$	$3$	$-2$
$y$	$-2$	$5$	$12$

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.