From the pair of linear equations in the following problems, and find their solution graphically.

Question : From the pair of linear equations in the following problems, and find their solution 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.

Solution :

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

Then the equations will be

x + y = 10 …….(1)

y = x + 4 …….(2)

Let us now draw the graph of the above two equations by finding the solutions of equations.

For equation x + y = 10

x08
y = 10 – x102
PointsAB

For equation y = x + 4,

x013
y = x + 4457
PointsCDE

Now plot these points on graph :

The two lines AB and CE shown in the graph intersect at point E(3, 7). So, x = 3 and y = 7 is the required solution of the pair of linear equations.

i.e. Number of Boys = 3, Number of girls = 7

(ii) Let x be the cost of one pencil and y be the cost of one pen. Then the equation formed will be

5x + 7y = 50

and 7x + 5y = 46

Let us now draw the graph of the above two equations by finding the solutions of equations.

For equation 5x + 7y = 50,

x103
y05

For equation 7x + 5y = 46,

x83
y-25

Now plot these points on graph :

The two lines as shown in the graph intersect at point (3, 5). So, x = 3 and y = 5 is the required solution of the pair of linear equations.

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