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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006417
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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.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Solution

Let present age of Aftab be x years and present age of his daughter be y years.

Case I. Seven years ago,

Age of Aftab = (x - 7) years

Age of his daughter = (y - 7) years

According to question :

(x - 7) = 7 (y - 7)

⇒ x - 7 = 7y - 49

⇒ x - 7y = -42

Case II.

Three years later,

Age of Aftab = (x + 3) years

Age of his daughter = (y + 3) years

Accoring to questions,

x + 3 = 3 (y + 3)

⇒ x + 3 = 3y + 9

⇒ x — 3y = 6

So, algebraic expression be

x - 7y = -42    ...(i)

x - 3y = 6    ...(ii)

Graphical representation

For eq. (i), we have

x - 7y = -42

⇒    x — 7y — 42

Thus, we have following table :

From eqn. (ii), we have

x -3y = 6

⇒    x = 3y + 6

Thus, we have following table

When we plot the graph of equations. We find that both the lines intersect at the point (42, 12). Therefore, x = 42, y = 12 is the solution of the given system of equations.

Fig. 3.1.

Some More Questions From Pair of Linear Equations in Two Variables Chapter

Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x + y – 6 = 0,      4x – 2y – 4 = 0

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