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
| x | 0 | 8 |
| y = 10 – 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.
