Solve for x and y : …

On dividing each of the given equations by xy, we get
{tex}\frac { 6 } { y } + \frac { 3 } { x } = 7{/tex}.......(i)
{tex}\frac { 3 } { y } + \frac { 9 } { x } = 11{/tex}.....(ii)
Putting {tex}\frac 1x{/tex} = u and {tex}\frac 1y{/tex} = v in (i) and (ii), we get
{tex}6v + 3u = 7{/tex}..... (iii)
{tex}3v + 9u = 11{/tex}.. ..(iv)
Multiplying (iii) by 3 and subtracting (iv) from the result, we get
{tex}18v - 3v = 21 - 11{/tex}
{tex}\Rightarrow{/tex} {tex}15v = 10{/tex}
{tex}\Rightarrow \quad v = \frac { 10 } { 15 } = \frac { 2 } { 3 }{/tex}
Putting v = {tex}\frac 23{/tex} in (iii), we get
{tex}\left( 6 \times \frac { 2 } { 3 } \right) + 3 u = 7{/tex}{tex}\Rightarrow 4 + 3 u = 7 \Rightarrow 3 u = 3 \Rightarrow u = 1{/tex}
{tex}u = 1{/tex} {tex}\Rightarrow \frac { 1 } { x } = 1 \Rightarrow x = 1{/tex}
{tex}v = \frac { 2 } { 3 } \Rightarrow \frac { 1 } { y } = \frac { 2 } { 3 }{/tex}{tex}\Rightarrow 2 y = 3 \Rightarrow y = \frac { 3 } { 2 }{/tex}
{tex}\therefore{/tex}  {tex}x = 1\ and\ y = {/tex}{tex}\frac 32{/tex}