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Form the pair of linear equations in the following problems, and find their (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.

Q1.    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.

Answers (1)
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Let the number of boys be x and the number of girls be y. 

Now, According to the question,

Total number of students in the class = 10, i.e.

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

And

the number of girls is 4 more than the number of boys,i.e.

x=y+4

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

Different points (x, y) for equation (1)

X 5 6 4
Y 5 4 6

Different points (x,y) satisfying (2)

X 5 6 7
y 1 2 3

 

Graph,

As we can see from the graph, both lines intersect at the point (7,3). that is x= 7 and y = 3 which means the number of boys in the class is 7 and the number of girls in the class is 3.

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