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 โฆโฆ.(1)
y = x + 4 โฆโฆ.(2)
Let us now draw the graph of the above two equations by finding the solutions of equations.
For equation x + y = 10
x
0
8
y = 10 โ x
10
2
Points
A
B
For equation y = x + 4,
x
0
1
3
y = x + 4
4
5
7
Points
C
D
E
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,
x
10
3
y
0
5
For equation 7x + 5y = 46,
x
8
3
y
-2
5
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.