Question

5/X+1 - 2/y-1 = 1/2, 10/X+1 +2/y-1 = 5/2 . By Substituting Method​

Answer 1

Answer

$\sf \dashrightarrow \dfrac{5}{x + 1} - \dfrac{2}{y - 1} = \dfrac{1}{2} \: \: --- (i)$

$\sf \dashrightarrow \dfrac{10}{x + 1} + \dfrac{2}{y - 1} = \dfrac{5}{2} \: \: --- (ii)$

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

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

So, the equations become,

$\sf \dashrightarrow 5u - 2v = \dfrac{1}{2}$

and

$\sf \dashrightarrow 10u + 2v = \dfrac{5}{2}$

By equation i,

$\sf \dashrightarrow 5u - 2v = \dfrac{1}{2}$

$\sf \dashrightarrow 5u = \dfrac{1}{2} + 2v$

$\sf \dashrightarrow 5u = \dfrac{1 + 4v}{2}$

$\sf \dashrightarrow u = \dfrac{1 + 4v}{2} \times \dfrac{1}{5}$

$\sf \dashrightarrow u = \dfrac{1 + 4v}{10}$

Now, we should find the value of y by second equation.

$\sf \dashrightarrow 10u + 2v = \dfrac{5}{2}$

$\sf \dashrightarrow 10 \bigg( \dfrac{1 + 4v}{10} \bigg) + 2v = \dfrac{5}{2}$

$\sf \dashrightarrow \dfrac{10 + 40v}{10} + 2v = \dfrac{5}{2}$

$\sf \dashrightarrow \dfrac{10 + 40v + 20v}{10} = \dfrac{5}{2}$

$\sf \dashrightarrow \dfrac{10 + 60v}{10} = \dfrac{5}{2}$

$\sf \dashrightarrow 10 + 60v = \dfrac{5}{2} \times 10$

$\sf \dashrightarrow 10 + 60v = \dfrac{50}{2}$

$\sf \dashrightarrow 60v = 25 - 10$

$\sf \dashrightarrow 60v = 15$

$\sf \dashrightarrow v = \dfrac{15}{60}$

$\sf \dashrightarrow v = \dfrac{1}{4}$

Now, let's find the value of u.

$\sf \dashrightarrow 5u - 2v = \dfrac{1}{2}$

$\sf \dashrightarrow 5u - 2 \bigg( \dfrac{1}{4} \bigg) = \dfrac{1}{2}$

$\sf \dashrightarrow 5u - \dfrac{2}{4} = \dfrac{1}{2}$

$\sf \dashrightarrow 5u = \dfrac{1}{2} + \dfrac{2}{4}$

$\sf \dashrightarrow 5u = \dfrac{2 + 2}{4}$

$\sf \dashrightarrow 5u = \dfrac{4}{4}$

$\sf \dashrightarrow 5u = 1$

$\sf \dashrightarrow u = \dfrac{1}{5}$

Now, let's find the values of x and y.

We know that,

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

$\sf \dashrightarrow \dfrac{1}{x} = \dfrac{1}{5}$

$\sf \dashrightarrow x = 5$

We also know that,

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

$\sf \dashrightarrow \dfrac{1}{y} = \dfrac{1}{4}$

$\sf \dashrightarrow y = 4$

Hence, the values of x and y are 5 and 4 respectively.