-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 ♬ ♬