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.


(i) Let number of boys = x

Let number of girls = y


According to the question,


=


=


Putting y = 0 , 5, 10 . we get,


X = 10 – 0 = 10


X = 10 – 5 = 5


X = 10 – 10 = 0


x



10



5



0



y



0



5



10



Number of girls is 4 more than number of boys …………Given


So,


Y = x + 4


Putting x = -4 ,0 , 4 we get,


Y = -4+4 = 0


Y= 0 + 4 = 4


Y = 4 + 4 = 8


x



-4



0



4



Y



0



4



8



Graphical representation :



(ii) Let cost of one pencil = Rs. X


Let cost of one pen = Rs. Y


According to the question,


=


=


=


Putting value of y = 5 , 10 , 15 we get,


X =


X =


X =


x



3



-4



-11



Y



5



10



15



Now,


7 pencils and 5 pens together cost Rs. 46


7x + 5y = 46


= 5y = 46 – 7x


= y = 9.2 – 1.4x


Putting x = 0 , 2 , 4 we get,


Y= 9.2 – 1.4×0 = 9.2


Y = 9.2 – 1.4 × 2 = 9.2 – 2.8 = 6.4


Y = 9.2 – 1.4 × 4 = 9.2 – 5.6 = 3.6


x



0



2



4



y



9.2



6.4



3.6



Graphical Representation:



1
1