X + ✅y =7 and ✔x …

Given equations are
{tex}\frac{x}{4}{/tex} + {tex}\frac{2y}{3} = 7{/tex}...............(i)
and {tex}\frac{x}{6}{/tex} + {tex}\frac{3y}{5} = 11{/tex} .................(ii)
From equation (i), we get
{tex}\frac{x}{4}{/tex} + {tex}\frac{2y}{3} = 7{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{x}{4}{/tex} = 7 - {tex}\frac{2y}{3}{/tex}
{tex}\Rightarrow{/tex} {tex} x = 4(7 -\frac{2y}{3}){/tex}
{tex}\Rightarrow{/tex} x = 28 - {tex}\frac{8y}{3}{/tex}.................(iii)
substituting x = 28 - {tex}\frac{8y}{3}{/tex} in equation (ii), we get
{tex}\frac { 28 - \frac { 8 y } { 3 } } { 6 } + \frac { 3 y } { 5 } = 11{/tex}
 {tex}\Rightarrow{/tex} {tex}\frac { 84 - 8 y } { 18 } + \frac { 3 y } { 5 } = 11{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{420 - 40y + 54y}{18 \times 5}{/tex} = 11
{tex}\Rightarrow{/tex} 420 + 14y = 990
{tex}\Rightarrow{/tex} 14y = 570
{tex}\Rightarrow{/tex} y = {tex}\frac{570}{14}{/tex} = {tex}\frac{285}{7}{/tex}
When y = {tex}\frac{285}{7}{/tex}, equation (iii) becomes
{tex}x = 28 - \frac { 8 \times \frac { 285 } { 7 } } { 3 }{/tex}
{tex}\Rightarrow{/tex} {tex} x = 28 -\frac{8 \times 285}{21}{/tex}
{tex}\Rightarrow{/tex}  {tex}x = \frac{588 - 2280}{21}{/tex} = {tex}\frac{-1692}{21}{/tex}
{tex}\Rightarrow{/tex}  -{tex}x =\frac{564}{7}{/tex}
{tex}\therefore{/tex} x = -{tex}\frac{564}{7}{/tex}, y = {tex}\frac{285}{7}{/tex} is the solution of given system of equations.