ravish tells his daughter aarushi,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'.if present ages of aarushi and ravish are x and yyearsrespectively,represent this situation algebraically and graphically.

Given, present ages of Aarushi and Ravish are *x* and *y* years respectively.

Seven years ago,

Age of Aarushi = (*x* – 7) years

Age of Ravish = (*y* – 7) years

Age of Ravish = 7 × Age of Aarushi

∴* y* – 7 = 7 (*x* – 7)

*⇒ y* – 7 = 7*x* – 49

*⇒ *7*x* – *y* = 42 ...(1)

Three years hence,

Age of Aarushi = (*x* + 3) years

Age of Ravish = (*y* + 3) years

Age of Ravish 3 × Age of Aarushi

∴ *y* + 3 = 3 (*x* + 3)

*⇒ y* + 3 = 3*x* + 9

*⇒ *3*x* – *y* = – 6 ...(2)

The given situation can be represented algebraically by the system of simultaneous equation given by 7*x* – *y* = 42 and 3*x* – *y* = 6.

Consider the equation

7*x* – *y* = 42.

∴ *y* = 7*x* – 42

When *x* = 6, *y *= 7 × 6 – 42 = 42 – 42 = 0

When *x* = 7, *y* = 7 × 7 – 42 = 49 – 42 = 7

When *x* = 5, *y* = 7 × 5 – 42 = 35 – 42 = – 7

These points can be represented in a table as,

x | 6 | 7 | 5 |

y | 0 | 7 | – 7 |

Consider the equation

3*x* – *y* = – 6

∴ *y *= 3*x *+ 6

When *x* = – 2, *y *= 3 × (– 2) + 6 = – 6 + 6 = 0

When *x* = – 1, *y* = 3 × (– 1) + 6 = – 3 + 6 = 3

When *x* = 0, *y* = 3 × 0 + 6 = 0 + 6 = 6

These points can represented in table as,

x | – 2 | – 1 | 0 |

y | 0 | 3 | 6 |

The given situation can be represented graphically as,

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