Form the pair of linear equations in the problem, and find it's solution graphically.
10 students of class X took part in 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.
Formulation: Let the number of girls be x and the number of boys be y.
It is given that total ten students took part in the quiz.
$\therefore$ Number of girls+ Number of boys = 10
i.e. x + y =10
It is also given that the number of girls is 4 more than the number of boys.
$\therefore$ Number of girls= Number of boys + 4
i.e. x = y+4
or, x-y = 4
Thus, the algebraic representation of the given situation is
x + y=10 ........(i)
x - y =4 ..........(ii)
Add (i) and (ii) we get
x + y + x - y = 10 + 4
2x = 14
x = 7
Put x = 7 in (i)
x + y = 10
7 + y = 10
y = 10 -7
y = 3
So, value of x = 7 and y = 3
Graphical Representation: Now putting y = 0 in x + y = 10, we get
x = 10. Similarly, by putting x = 0 in x + y = 10, we get y = 10.
Thus, two solution of equation (i) are:
| x | 10 | 0 |
| y | 0 | 10 |
Similarly, two solutions of equation (ii) are:
putting y = 0 in x - y = 4, we get
x = 4. Similarly, by putting x = 0 in x + y = 10, we get y = -4.
| x | 4 | 0 |
| y | 0 | -4 |
Now, we plot the points A (10, 0), B (0, 10), P (4, 0) and Q (0, -4) corresponding to these solutions on the graph paper and draw the lines AB and PQ representing the equations x + y = 10 and x - y - 4 as shown in Fig.
![](https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/5236/TTam22a.png")
We observe that the two lines representing the two equations are intersecting at the point (7, 3).
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