$$ \frac{3}{x}-\frac{2}{y}=0 \quad .....(1) $$
$$ \frac{2}{x}+\frac{5}{y}=19 \quad .....(2) $$
Multiplying equation no. $$ (1) $$ by $$ 5 $$ and $$ (2) $$ by $$ 2 $$.
$$ \frac{15}{x}-\frac{10}{y}=0 \quad ....(3) $$
$$ \frac { \frac { 4 }{ x } +\frac { 10 }{ y } =38 }{ \frac { 19 }{ x } =38}\quad \quad \quad \quad \Rightarrow x=\frac { 1 }{ 2 }.....(4) $$
From $$ (1)3\left( \frac { 1 }{ 2 } \right) -\frac{2}{y}=0 \quad \quad \quad \Rightarrow y=\frac{1}{3} $$
$$ \therefore y=ax+3 $$
$$ \frac{1}{3}=a\left( \frac { 1 }{ 2 } \right) +3 $$
$$ \frac{a}{2}=\frac{-8}{3}\Rightarrow a=\frac{-16}{3} $$