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.

Ans. (i)Let the number of boys and girls who took part in quiz be x and y respectively.

According to the given statement in the question:

=>\(x + y = 10)\)............(1)

Points which lie on the equation (1) are :

\(\begin{array} {|r|r|}\hline x & 0 & 10 \\ \hline y & 10 & 0 \\ \hline \end{array}\)

According to the given statement in the question:

=>\(x - y = -4)\)............(2)

Solutions of the equation (2) are :

\(\begin{array} {|r|r|}\hline x & 0 & -4 \\ \hline y & 4 & 0 \\ \hline \end{array}\)

Now the graph for the above equations (1) and (2) will be:



From the graph it is visible that equation (1) and (2) intersect at \((3,7)\)

Therefore, number of boys who took part in quiz = 3 and, number of girls who took part in quiz = 7.

(ii)Let the cost of one pencil and cost of one pen be Rs.x and Rs.y respectively.

According to the given statement in the question:


=>\(5x + 7y = 50\)............(1)

Points which lie on the equation (1) are :

\(\begin{array} {|r|r|}\hline x & 10 & 3 \\ \hline y & 0 & 5 \\ \hline \end{array}\)

According to the given statement in the question:

=>\(7x + 5y = 46\)............(2)

Solutions of the equation (2) are :

\(\begin{array} {|r|r|}\hline x & 8 & 3 \\ \hline y & -2 & 5 \\ \hline \end{array}\)

Now the graph for the above equations (1) and (2) will be:



From the graph it is visible that equation (1) and (2) intersect at \((3,5)\)

Therefore, cost of pencil = Rs.3 and, Cost of pen = Rs.5.