1.

A fraction becomes 1/3, if 2 is added to both of its numerator and denominator. If 3 is added to both of its numerator and denominator then it becomes 2/5.Form a linear equation to represent it.​

Answer»

Answer:

3x - y = - 4

5x - 2y = - 9            , moreover

  fraction = x/y = 1/7

Step-by-step EXPLANATION:

Let the numerator be 'x' and denominator be 'y'. Thus, fraction be x/y.

if 2 is ADDED to both of its numerator and denominator, fraction becomes 1/3:

⇒ (x + 2)/(y + 2) = 1/3

⇒ 3(x + 2) = y + 2

⇒ 3x - y = - 4        ...(1)

If 3 is added to both of its numerator and denominator then it becomes  2/5.

⇒ (x + 3)/(y + 3) = 2/5

⇒ 5(x + 3) = 2(y + 3)

⇒ 5x - 2y = - 9       ...(2)

These TWO equations(linear) represent the given conditions, where x is numerator and y is denominator.

from (1), y = 3x + 4,   SUBSTITUTE in (2):

=> 5x - 2y = - 9       ⇒ 5x - 2(3x+4) = -9

=> x = 1        and thus y = 3(1) + 4 = 7


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