1/7x+ 1/6y=3 1/2x-1/3y=5

{tex}\frac{1}{7x}{/tex} + {tex}\frac{1}{6y}{/tex} = 3 .......(i)
and {tex}\frac{1}{2x}{/tex} - {tex}\frac{1}{3y}{/tex} = 5 ...........(ii)
Multiplying equation (ii) by {tex}\frac{1}{2}{/tex}, we get
 {tex}\frac{1}{4x}{/tex} - {tex}\frac{1}{6y}{/tex} = {tex}\frac{5}{2}{/tex} ..........(iii)
Adding eq. (i) and (iii), we get
{tex}\frac{1}{4x}{/tex} + {tex}\frac{1}{7x}{/tex} = {tex}\frac{5}{2}{/tex} + 3
{tex}\Rightarrow{/tex} {tex}\frac{7 + 4}{28x}{/tex} = {tex}\frac{11}{2}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac{11}{28x}{/tex} = {tex}\frac{11}{2}{/tex}
{tex}\Rightarrow{/tex} 28x = 2 
{tex}\Rightarrow{/tex} x = {tex}\frac{1}{14}{/tex}
Putting the value of x in eq.(i), we get
{tex}\frac{1}{7(\frac1{14})}{/tex} + {tex}\frac{1}{6y}{/tex} = 3
y = {tex}\frac{1}{6}{/tex}
Hence x = {tex}\frac{1}{14}{/tex} and y = {tex}\frac{1}{6}{/tex} is the solution of given system of equations.