Please explain the formation of equations.
Explain the graph of this question.
Class 10th rd sharma, pair of linear equations in two variables.
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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.
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Solution:
Let the present age of Aftab and his daughter be x and y, respectively.
Hence, seven years ago,
Age of Aftab = x – 7 and Age of his daughter = y – 7
According to the given condition,
x – 7 = 7 (y – 7) ⇒ x – 7y = -42……… (i)
Three years from the present age,
x + 3 = 3 (y + 3) ⇒x – 3y = 6………..(ii)
Therefore, equations (i) and (ii) represent the situation algebraically.
To represent these equations graphically, we need at least two solutions for each (i) and (ii).
And let’s put them on a table for each.
For equation (i),
For equation (ii),
The above can be plotted in a graph as below: