Solve xy/x+y=1/5 , xy/x+y =1/7

{tex}\frac{xy}{x + y}{/tex} = {tex}\frac{1}{5}{/tex} {tex}\Rightarrow{/tex} {tex}\frac{x + y}{xy}{/tex} = {tex}\frac{5}{1}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac{1}{y}{/tex}+ {tex}\frac{1}{x}{/tex} {tex}= 5{/tex}....(i)
and {tex}\frac{xy}{x - y}{/tex} = {tex}\frac{1}{7}{/tex} {tex}\Rightarrow{/tex} {tex}\frac{x - y}{xy}{/tex} {tex}= 7{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{1}{y}{/tex} - {tex}\frac{1}{x}{/tex} = 7...(ii)
Now solve equation (i) and (ii) by assuming {tex}\frac{1}{y}{/tex} {tex}= a{/tex} and {tex}\frac{1}{x}{/tex} {tex}= b{/tex}
{tex}\therefore{/tex} eq.(i) and (ii) becomes

{tex}\Rightarrow{/tex}{tex}b = -1{/tex}.....(iii)
Putting the value of {tex} b = -1{/tex} from eq. (iii) in equation (i), we get
{tex}a - 1 = 5{/tex} {tex}\Rightarrow{/tex} {tex}a = 6{/tex}
Now, {tex}\frac{1}{y}{/tex} {tex}= 6{/tex} {tex}\Rightarrow{/tex} {tex}y ={/tex} {tex}\frac{1}{6}{/tex}
and {tex}\frac{1}{x}{/tex} = -1 {tex}\Rightarrow{/tex} {tex}x = -1{/tex}