Question

A fraction becomes 9/11 if 3 is added to both numerator and denominator. If 2 is added to both numerator and denominator, it becomes 4/6. Form the pair of linear equation for the above situation.​

Answer 1

GIVEN :–

• When 3 is added to both numerator and denominator , Fraction becomes 9/11 .

• When 2 is added to both numerator and denominator, it becomes 4/6.

TO FIND :–

• The pair of linear equation = ?

SOLUTION :–

• Let the fraction is $\:\:{ \bold{ \dfrac{x}{y}}} \:\:$

• According to the first condition –

$\\ \implies{ \bold{ \dfrac{x + 3}{y + 3} = \dfrac{9}{11} }} \:\:$

$\\ \implies{ \bold{ 11(x + 3) = 9(y + 3)}} \:\:$

$\\ \implies{ \bold{ 11x + 33= 9y + 27}} \:\:$

$\\ \implies{ \bold{ 11x - 9y= - 33 + 27}} \:\:$

$\\ \implies{ \bold{ 11x =9y - 6}} \:\:$

$\\ \implies{ \bold{ x = \dfrac{1}{11} (9y - 6) \: \: \: - - - eq.(1)}} \:\:$

• According to the second condition –

$\\ \implies{ \bold{ \dfrac{x + 2}{y + 2} = \dfrac{4}{6} }} \:\:$

$\\ \implies{ \bold{ 6(x + 2) = 4(y + 2)}} \:\:$

$\\ \implies{ \bold{ 6x + 12= 4y + 8}} \:\:$

$\\ \implies{ \bold{ 6x - 4y= 8 - 12}} \:\:$

$\\ \implies{ \bold{6x - 4y= - 4 \: \: \: \: \: - - - eq.(2)}} \:\:$

• eq.(1) and eq.(2) are required linear equations.

Answer 2

ANSWER

$</p><p>\sf Let \: the \: fraction \: be \: \frac{x}{y}$

$\frac{x + 3}{y + 3} = \frac{9}{11}$

$11(x + 3) = 9(y + 3)$

$11x + 33 = 9y + 27$

$11x - 9y = 27 - 33$

$11x - 9y = - 6$

$11x - 9y + 6 = 0$⠀⠀⠀⠀...(i)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\frac{x + 2}{y + 2} = \frac{4}{6}$

$6(x + 2) = 4(y + 2)$

$6x + 12 = 4y + 8$

$6x - 4y = 8 - 12$

$6x - 4y = - 4$

$6x - 4y + 4 = 0$⠀⠀⠀⠀...(ii)

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From (i) & (ii) the pair of linear equations formed are:-

❶ 11x - 9y + 6 = 0

❷ 6x - 4y + 4 = 0

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