Question

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." Is not this interesting? Represent this situation algebraically and graphically.

Answer 1

Concept :

To draw the graph of a linear equation in two variable a series of steps to be followed which is given below:

• Step I:Obtain the linear equation.  Let the equation be  ax + by + c = 0
• Step II: Express one unknown quantity in terms of other here. Express y in terms of x to get y = - (ax + c /b)
• Step III: For any two values of x, calculate the corresponding values of y  from the expression in step II to obtain two solutions say (x1, y1 and( x2 ,y2)
• Step IV: plot the points  (x1, y1 and( x2 ,y2)  on graph paper on a suitable scale.
• Step V:Draw a  line passing through points marked in step IV. The line so obtained is the graph of the equation  ax + by + c = 0  

 

Given: 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."  

Solution :

Let the age of Aftab be x years and  Aftab's daughter by y years

 

 Condition: 1

 ( x - 7 ) = 7 ( y - 7 )

 ( x - 7 ) = 7y - 49

 x - 7 - 7y + 49

 x - 7y + 42 = 0  or x - 7y  = - 42 …………..(1)

 

Condition: 2

 ( x + 3 ) = 3 ( y + 3 )

 ( x + 3 ) = 3y + 9

 x + 3 - 3y +  9

 x - 3y - 6 = 0   or x - 3y = 6………….. (2)

 

Hence , algebraically it is represented by :

x - 7y + 42 = 0  or x - 7y  = - 42

and x - 3y - 6 = 0   or x - 3y = 6

Table and the Graph ( Geometrically) of the given  systems of equations are in the  attachment below :  

x - 7y  = - 42, passes through (7, 7) and (14,8), (21, 9)

x - 3y = 6, passes through (9,1) and (12, 2), (15,3)

Hope this answer will help you…

 

Some more questions from this chapter :  

Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs Rs 3, and a game of Hoopla costs Rs 4. If she spent Rs 20 in the fair, represent this situation algebraically and graphically.

https://brainly.in/question/15918159

 

Solve the following systems of equations graphically:

x-2y=5

2x+3y=10

https://brainly.in/question/15918170

Answer 2

Answer:

hope the above image helps you ✌️✌️