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# 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.