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Exercise - 3.1

Pair of Linear Equations in two Variables

**Question-1 :-** Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Let us denote age of Aftab x and age of his daughter y. Then the algebraic representation is given by the following equations: x – 7 = 7 (y – 7) x - 7 = 7y - 49 x - 7y = -49 + 7 x - 7y = -42 .......(i) x + 3 = 3 (y + 3) x + 3 = 3y + 9 x - 3y = 9 - 3 x - 3y = 6 ......(ii) Lets represent these equations in graphically: x - 7y = -42 .......(i)

x | 0 | 7 |

y | 6 | 7 |

x | 0 | 6 |

y | -2 | 0 |

**Question-2 :-** The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Represent this situation algebraically and geometrically.

Let x and y be the bats and balls. 3x + 6y = 3900 x + 2y = 1300 .......(i) x + 2y = 1300 ........(ii) Lets represent these equations in graphically: x + 2y = 1300 .......(i)

x | 0 | 1300 |

y | 650 | 0 |

x | 0 | 1300 |

y | 650 | 0 |

**Question-3 :-** The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160.
After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and geometrically.

Let us denote apples by x and grapes by y. The algebraic representation is given by the following equations: 2x + y = 160 ...........(i) 4x + 2y = 300 2x + y = 150...........(ii) Lets represent these equations in graphically: 2x + y = 160 ...........(i)

x | 50 | 60 |

y | 60 | 40 |

x | 70 | 75 |

y | 10 | 0 |

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