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 50, whereas 7 pencils and 5 pens together cost 46. Find the cost of one pencil and that of one pen.
(i) Let there are x number of girls and y number of boys. As per the given question, the algebraic expression can be represented as follows.
x + y = 10
x– y = 4
Now, for x + y = 10 or x = 10 - y, the solutions are
x → 5, 4, 6
y → 5, 6, 4
For x – y = 4 or x = 4 + y, the solutions are
x → 4, 5, 3
y → 0, 1, -1
The graphical representation is as follows
(ii)Let 1 pencil costs Rs. x and 1 pen costs Rs. y.
According to the question, the algebraic expression cab be represented as;
5x + 7y = 50
7x + 5y = 46
For, 5x + 7y = 50 or x = (50-7y)/5, the solutions are
x → 3, 10, -4
y → 5, 0, 10
For 7x + 5y = 46 or x = (46-5y)/7, the solutions are
x → 8, 3, -2
y → -2, 5, 12
Hence, the graphical representation is as follows
From the graph, it is can be seen that the given lines cross each other at point (3, 5).
So, the cost of a pencil is 3/- and cost of a pen is 5/-.