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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006902
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Manish says to Rahim “I am three times as old as you are.” Later Manish says to Rahim “After 5 years I shall be two times as old as you will be.” Represent this situation algebraically and graphically.

Solution

Let present age of Manish be x years and present age of Rahim be y years.
Case I.    x = 3y
⇒    x - 3y = 0
Case II.
After 5 years :
Age of Manish = (x + 5) years
Age of Rahim = {y + 5) year

Fig. 3.18.
According to question
x + 5 = 2(y + 5)
⇒    x + 5 = 2y + 10
⇒    x - 2y = 10 - 5
⇒    x - 2y = 5
So, algebraic representation be
x - 3y = 0    ...(i)
x - 2y = 5    ...(ii)
Graphical representation
For eqn. (i), we have
x - 3y = 0
⇒    x = 3y
Thus, we have following table :

For eqn. (ii), we have
x - 2y = 5
⇒    x = 5 + 2y
Thus, we have following tables :

When we plot the graph of the equation, we find that both the lines intersect at one point.
Hence, given system of equations has a unique solution.
So, we can say that system is consistent.

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