-1/5y-1/2=-3/7

I believe you made a slight transcription error, Melody........you typed -3/5 but you meant -3/7.....

Start by adding 1/2 to both sides so we would have

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

We need a common denominator

(-1/5)y=-6/14+7/14

(-1/5)y=1/14

Multiply by -5

y=-5/14

  -1/5y-1/2=-3/7  

The lowest common denominator is 70 so mult everything by 70

$$\begin{array}{rll}
\\70\left(\frac{-1y}{5}-\frac{1}{2}\right)&=&70\times \frac{-3}{7}\\\\
-14y-35&=&-30\\\\
-14y&=&5\\\\
y&=&\frac{-5}{14}
\end{array}$$

$$\textstyle{
\begin{array}{rcl}
-\dfrac{1}{5}y-\dfrac{1}{2}&=&-\dfrac{3}{7} \quad | \quad \times(-1)\\\\
\dfrac{1}{5}y+\dfrac{1}{2} &=&\dfrac{3}{7} \\\\
\dfrac{2y+5}{10} &=&\dfrac{3}{7} \quad | \quad \times 10\\\\
2y+5 &=&\dfrac{30}{7} \quad | \quad -5\\\\
2y&=&\dfrac{30}{7}-5*\dfrac{7}{7}=-\dfrac{5}{7}\\\\
y&=&-\dfrac{5}{14}
\end{array}
}$$

Thanks Chris.      .♬ ♬ MELODY ♬ ♬