\(5x-3y=2\)

\(\frac{6}{5}y+7y=-\frac{4}{5}+3\)

\(\frac{41}{5}y=\frac{11}{5}\)

\(y=\frac{11}{5}\cdot\frac{5}{41}=\frac{11}{41}\)

\(5x-3\cdot\frac{11}{41}=2\)

\(5x-\frac{33}{41}=2\)

\(5x=2+\frac{33}{41}=\frac{115}{41}\)

\(x=\frac{23}{41}\)

Result: \((x,y)=(\frac{23}{41},\frac{11}{41})\)