Question

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Answer 1

Answer:

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Answer 2

Answer

$\sf \dashrightarrow \dfrac{11}{x} - \dfrac{7}{y} = 1 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{9}{x} - \dfrac{4}{y} = 6 \: \: --- (ii)$

Let $\sf \dfrac{1}{x}$ be u.

Let $\sf \dfrac{1}{y}$ be v.

So, the equations become

$\sf \dashrightarrow 11u - 7v = 1$

$\sf \dashrightarrow 9u - 4v = 6$

By first equation,

$\sf \dashrightarrow 11u - 7v = 1$

$\sf \dashrightarrow 11u = 1 + 7v$

$\sf \dashrightarrow u = \dfrac{1 + 7v}{11}$

Now, let's find the value of v by second equation.

$\sf \dashrightarrow 9u - 4v = 6$

$\sf \dashrightarrow 9 \bigg( \dfrac{1 + 7v}{11} \bigg) - 4v = 6$

$\sf \dashrightarrow \dfrac{9 + 63v}{11} - 4v = 6$

$\sf \dashrightarrow \dfrac{9 + 63v - 44v}{11} = 6$

$\sf \dashrightarrow \dfrac{9 + 19v}{11} = 6$

$\sf \dashrightarrow 9 + 19v = 11 \times 6$

$\sf \dashrightarrow 9 + 19v = 66$

$\sf \dashrightarrow 19v = 66 - 9$

$\sf \dashrightarrow 19v = 57$

$\sf \dashrightarrow v = \dfrac{57}{19}$

$\sf \dashrightarrow v = 3$

Now, let's find the value of u by first equation.

$\sf \dashrightarrow 11u - 7v = 1$

$\sf \dashrightarrow 11u - 7(3) = 1$

$\sf \dashrightarrow 11u - 21 = 1$

$\sf \dashrightarrow 11u = 1 + 21$

$\sf \dashrightarrow 11u = 22$

$\sf \dashrightarrow u = \dfrac{22}{11}$

$\sf \dashrightarrow u = 2$

We know that,

$\sf \dashrightarrow \dfrac{1}{x} = u$

$\sf \dashrightarrow \dfrac{1}{x} = 2$

$\sf \dashrightarrow 2x = 1$

$\sf \dashrightarrow x = \dfrac{1}{2}$

We also know that,

$\sf \dashrightarrow \dfrac{1}{y} = v$

$\sf \dashrightarrow \dfrac{1}{y} = 3$

$\sf \dashrightarrow 3y = 1$

$\sf \dashrightarrow y = \dfrac{1}{3}$

Hence, the values of x and y are 1/2 and 1/3 respectively.