Question

S44,0)
used to look for solutions of the pair
of linear equations.
Fig. 3.4
EXERCISE 3.1
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.

Answer 1

Consider Aftab's age as x and his daughter's age as y.

Then , seven years ago,

Aftab's age =x−7

His daughter's age =y−7

According to the question,

x−7=7(y−7)

x−7=7y−49

x−7y=−49+7 

 x−7y=−42                    …(i)

After three years,

Aftab's age =x+3

His daughter's age =y+3

According to the question,

x+3=3(y+3)

x+3=3y+9

x−3y=9−3

x−3y=6                       …(ii)

Representing equation (i) and (ii) geometrically, we plot these equations by finding points on the lines representing these two equations

x−7y=−42⟹x=7y−42

 x=7y−42423549 y 121113

x−3y=6⟹x=3y+6

 x=3y+6 42 3648 y 121014

From the graph we can see that two lines will intersect at a point. 

 x−7y=−42   

x−3y=6  

On subtracting the two equations, we get 

4y=48

or =12

Substituting value of y in (2), 

x−36=6

∴x=42

Hope this helps you

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