Question

solve it fast please​

Answer 1

hence X is 3 and y is 2

this is full answer

Answer 2

$\mathtt{SOLUTION:-}$

$\implies\tt\purple{ \frac{10}{x + y} + \frac{2}{x - y} = 4 }$

$\implies\tt\purple{ \frac{15}{x + y} - \frac{5}{x - y} = - 2 }$

$\implies\tt{LET \: \: \frac{1}{x + y} = a \: \: \: \: and \: \: \: \frac{1}{x - y} = b}$

$\implies\tt{NOW,}$

$\implies\tt\purple{10a + 2b - 4 = 0 \: \: \: \: eq(i)}$

$\implies\tt\purple{15a - 5b + 2 = 0 \: \: \: \: eq(ii)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{NOW, \: USING \: CROSS\: MULTIPLICATION \: METHOD}$

$\implies\tt\purple{ \frac{a}{4 - 20} = \frac{b}{ - 60 - 20} = \frac{1}{ - 50 - 30} }$

$\implies\tt\purple{ \frac{a}{ - 16} = \frac{b}{ -80} = \frac{1}{ - 80} }$

$\implies\tt\purple{ \frac{a}{ - 16} = \frac{1}{ - 80} }$

$\implies\tt\purple{ {a} = \frac{ - 16}{ - 80} }$

$\implies\tt\purple{a = \frac{1}{5} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies\tt\purple{ \frac{b}{ - 80} = \frac{1}{ - 80} }$

$\implies\tt\purple{b = 1}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies\tt\purple{ \frac{1}{x + y} = a}$

$\implies\tt\purple{ \frac{1}{x + y} = \frac{1}{5} }$

$\implies\tt\purple{x + y = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: eq(iii)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies\tt\purple{ \frac{1}{x - y} = \frac{1}{1} }$

$\implies\tt\purple{ \frac{1}{x - y} = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: eq(iv) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies\tt{NOW, \: USE \: ELIMINATION \: METHOD \: FOR \: EQ \: (iii) \: and \: (iv)}$

$\implies\tt\purple{x + y = 5}$

$\implies\tt\purple{x - y = 1}$

$\implies\tt\purple{2x = 6}$

$\implies\tt\purple{x = 3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies\tt\purple{x + y = 5}$

$\implies\tt\purple{3 + y = 5}$

$\implies\tt\purple{y = 2}$