{tex}mx – ny = m^2 + n^2{/tex} …(i){tex}x + y = 2m{/tex} …(ii)Multiplying equation (ii) by m and subtracting from (i), we get{tex}y = \\frac { n ^ { 2 } – m ^ { 2 } } { – ( m + n ) }{/tex}\xa0= -\xa0{tex}\\frac { ( n – m ) ( n + m ) } { m + n }{/tex}y = m – nPutting value of y in (i), we get{tex}mx – n(m – n) = m^2 + n^2{/tex}{tex}mx – nm + n^2 = m^2 + n^2\xa0{/tex}{tex}mx = m^2 + nm ={/tex}\xa0{tex}\\frac{m(m + n)}{m}{/tex}{tex}x = m + n{/tex}

{tex}mx – ny = m^2 + n^2{/tex} …(i){tex}x + y = 2m{/tex} …(ii)Multiplying equation (ii) by m and subtracting from (i), we get{tex}y = \\frac { n ^ { 2 } – m ^ { 2 } } { – ( m + n ) }{/tex}\xa0= -\xa0{tex}\\frac { ( n – m ) ( n + m ) } { m + n }{/tex}y = m – nPutting value of y in (i), we get{tex}mx – n(m – n) = m^2 + n^2{/tex}{tex}mx – nm + n^2 = m^2 + n^2\xa0{/tex}{tex}mx = m^2 + nm ={/tex}\xa0{tex}\\frac{m(m + n)}{m}{/tex}{tex}x = m + n{/tex}
{tex}mx – ny = m^2 + n^2{/tex} …(i){tex}x + y = 2m{/tex} …(ii)Multiplying equation (ii) by m and subtracting from (i), we get{tex}y = \\frac { n ^ { 2 } – m ^ { 2 } } { – ( m + n ) }{/tex}\xa0= -\xa0{tex}\\frac { ( n – m ) ( n + m ) } { m + n }{/tex}y = m – nPutting value of y in (i), we get{tex}mx – n(m – n) = m^2 + n^2{/tex}{tex}mx – nm + n^2 = m^2 + n^2\xa0{/tex}{tex}mx = m^2 + nm ={/tex}\xa0{tex}\\frac{m(m + n)}{m}{/tex}{tex}x = m + n{/tex}