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 cost of one bat = Rs *x*

Cost of one ball = Rs *y*

3 bats and 6 balls for Rs 3900 So that

3*x *+ 6*y* = 3900 … **(i)**

Dividing equation by 3, we get

*x *+ 2*y* = 1300

Subtracting 2*y* both side we get

*x* = 1300 – 2*y *

Putting *y* = -1300, 0 and 1300 we get

*x* = 1300 – 2 (-1300) = 1300 + 2600 = 3900

*x *= 1300 -2(0) = 1300 - 0 = 1300

*x* = 1300 – 2(1300) = 1300 – 2600 = - 1300

x |
3900 | 1300 | -1300 |

y |
-1300 | 0 | 1300 |

Given that she buys another bat and 2 more balls of the same kind for Rs 1300

So, we get

*x* + 2*y *= 1300 … **(ii)**

Subtracting 2y both side we get

*x *= 1300 – 2*y*

Putting *y* = - 1300, 0 and 1300 we get

*x* = 1300 – 2 (-1300) = 1300 + 2600 = 3900

*x *= 1300 – 2 (0) = 1300 - 0 = 1300

*x *= 1300 – 2(1300) = 1300 – 2600 = -1300

x |
3900 | 1300 | -1300 |

y |
-1300 | 0 | 1300 |

Algebraic representation

3*x *+ 6*y* = 3900 … **(i)**

*x *+ 2*y *= 1300 … **(ii)**

Graphical representation,

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 cost each kg of apples = Rs *x*

Cost of each kg of grapes = Rs *y*

Given that the cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160

So that

2 *x *+ *y *= 160 … **(i)**

2*x* = 160 - *y*

*x* = (160 – *y*)/2

Let *y* = 0 , 80 and 160, we get

*x* = (160 – ( 0 )/2 = 80

*x* = (160- 80 )/2 = 40

*x* = (160 – 2 × 80)/2 = 0

x |
80 | 40 | 0 |

y |
0 | 80 | 160 |

Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300

So we get

4*x* + 2*y *= 300 … **(ii)**

Dividing by 2 we get

2*x* + *y* = 150

Subtracting 2*x* both side, we get

*y *= 150 – 2*x*

Putting *x* = 0 , 50 , 100 we get

*y *= 150 – 2 × 0 = 150

*y *= 150 – 2 × 50 = 50

*y *= 150 – 2 × (100) = -50

x |
0 | 50 | 100 |

y |
150 | 50 | -50 |

Algebraic representation,

2*x *+ *y* = 160 … **(i)**

4*x* + 2*y* = 300 … **(ii)**

Graphical representation,

**Form the pair of linear equations in the following problems, and find their solutions 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.

Let number of boys = *x*

Number of girls = *y*

Given that total number of student is 10 so that

*x *+ *y *= 10

Subtract y both side we get

*x *= 10 – *y*

Putting *y *= 0 , 5, 10 we get

*x *= 10 – 0 = 10

*x *= 10 – 5 = 5

*x *= 10 – 10 = 0

x |
10 | 5 |

y |
0 | 5 |

Given that If the number of girls is 4 more than the number of boys

So that

*y *= *x *+ 4

Putting *x* = -4, 0, 4, and we get

*y *= - 4 + 4 = 0

*y *= 0 + 4 = 4

*y *= 4 + 4 = 8

x |
-4 | 0 | 4 |

y |
0 | 4 | 8 |

Graphical representation

**Form the pair of linear equations in the following problems, and find their solutions graphically.**

(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.

Let cost of pencil = Rs *x*

Cost of pens = Rs *y*

5 pencils and 7 pens together cost Rs 50,

So we get

5*x* + 7*y* = 50

Subtracting 7*y* both sides we get

5*x* = 50 – 7*y*

Dividing by 5 we get

*x* = 10 - 7 y /5

Putting value of *y* = 5 , 10 and 15 we get

*x* = 10 – 7 × 5/5 = 10 – 7 = 3

*x* = 10 – 7 × 10/5 = 10 – 14 = - 4

*x* = 10 – 7 × 15/5 = 10 – 21 = - 11

x |
3 | -4 | -11 |

y |
5 | 10 | 15 |

Given that 7 pencils and 5 pens together cost Rs 46

7*x* + 5*y* = 46

Subtracting 7*x* both side we get

5*y* = 46 – 7*x*

Dividing by 5 we get

*y* = 46/5 - 7*x*/5

y = 9.2 – 1.4*x*

Putting *x* = 0 , 2 and 4 we get

*y* = 9.2 – 1.4 × 0 = 9.2 – 0 = 9.2

*y* = 9.2 – 1.4 (2) = 9.2 – 2.8 = 6.4

*y* = 9.2 – 1.4 (4) = 9.2 – 5.6 = 3.6

x |
0 | 2 | 4 |

y |
9.2 | 6.4 | 3.6 |

Graphical representation

Therefore, cost of one pencil = Rs 3 and cost of one pen = Rs 5.