x/3 + y/4 =11 5x/6 - …

The given equations are
{tex}\frac { x } { 3 } + \frac { y } { 4 } = 11{/tex}
{tex}\frac { 5 x } { 6 } - \frac { y } { 3 } = - 7{/tex}
 Now {tex}\frac { x } { 3 } + \frac { y } { 4 } = 11{/tex}
 {tex}\Rightarrow{/tex}{tex}\frac { 4 x + 3 y } { 12 } = 11{/tex} (by taking LCM)
{tex}4x + 3y = 132{/tex} ......(i)
{tex}\frac { 5 x } { 6 } - \frac { y } { 3 } = - 7{/tex}
{tex}\frac { 5 x - 2 y } { 6 } = - 7{/tex}(by taking LCM)
{tex}5x - 2y = -42{/tex}.........(ii)
Multiplying (i) by 2 and (ii) by 3, we get
{tex}8x + 6y = 264{/tex} ........(iii)
{tex}15x - 6y = -126{/tex} ........(iv)
Adding (iii) from (iv), we get
{tex}23x = 138{/tex} {tex}\Rightarrow{/tex} {tex}x = 6{/tex}
Substituting x = 6 in (i),we get
{tex}4 \times 6 + 3 y = 132 \Rightarrow 3 y = 132 - 24{/tex}
{tex}3y = 108{/tex}
{tex}y = 36{/tex}
{tex}\therefore{/tex} Solution is {tex}x = 6, y = 36{/tex}