Mathematics
Form the pair of linear equations in the following problems, and find their solutions graphically.
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.
Answer
Let no. of boys be x and no. of girls be y.
Given,
Total students = 10
⇒ x + y = 10
⇒ y = 10 - x ……..(1)
Given,
No. of girls is 4 more than no. of boys.
⇒ y - x = 4
⇒ y = x + 4 ……….(2)
Table of values for equation (1),
| x | y |
|---|---|
| 5 | 5 |
| 6 | 4 |
| 7 | 3 |
Table of values for equation (2),
| x | y |
|---|---|
| 0 | 4 |
| 1 | 5 |
| 2 | 6 |
Steps of construction :
Plot the points (5, 5), (6, 4) and (7, 3) and join them to form equation (1).
Plot the points (0, 4), (1, 5) and (2, 6) and join them to form equation (2).
The lines intersect at K(3, 7), which is the required solution.
Hence, linear equation pair are x + y = 10 and y - x = 4, where x is no. of boys and y is no. of girls and no. of boys = 3 and no. of girls = 7.