**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.