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Answer :
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.