Solve for x and y: x/a …

{tex}\frac { x } { a } + \frac { y } { b } = 2{/tex}
{tex}\frac { b x + a y } { a b } = 2{/tex}
{tex}bx + ay = 2ab{/tex}........(i)
{tex}ax - by = (a^2 - b^2){/tex}...(ii)
Multiplying (i) by b and (ii) by a
{tex}b^2x + bay = 2ab^2{/tex}.............(iii)
{tex}a^2x - bay = a(a^2 - b^2){/tex}........(iv)
Adding (iii) and (iv),we get
{tex}b^2x + a^2x = 2ab^2 + a^3 - ab^2{/tex}
{tex}x(b^2 + a^2) =  2ab^2 + a^3 - ab^2{/tex}
{tex}x(b^2 + a^2) = ab^2 + a^3{/tex}
{tex}x(b^2 + a^2) =a(b^2 + a^2){/tex}
{tex}x = \frac { a \left( b ^ { 2 } + a ^ { 2 } \right) } { \left( b ^ { 2 } + a ^ { 2 } \right) } = a{/tex}
Putting x = a in (i),we get
{tex}b \times a + a y = 2 a b{/tex}
{tex}a y = 2 a b - a b \Rightarrow a y = a b{/tex} or y = b
{tex}\therefore{/tex} solution is x = a, y = b