Solve the system by the addition method. \[ \begin{array}{r} -5 x-7 y=-6 \\ 15 x+21 y=19 \end{array} \]

Step 1 ：We can find $x$ by adding three times the first equation to the second. From \begin{align*}3(-5x-7y)+15x+21y&=-15x+45x\&=30x,\end{align*}and \begin{align*}3(-5x-7y)+15x+21y&=3(-6)+19\&=-18+19\&=1,\end{align*}we find that $30x = 1$, or $x=\frac{1}{30}.$

Step 2 ：Substituting into the second equation, we can find $y:$ \begin{align*}15x+21y&=19 \ \implies y&=\frac{1}{21}(19-15(\frac{1}{30}))\&=\frac{1}{21}(19-\frac{1}{2})\&=\frac{1}{21}(18.5)\&=\frac{37}{60}.\end{align*}

Step 3 ：Thus our answer is $\boxed{(\frac{1}{30},\frac{37}{60})}.$