jmc

To find the intersection, we must find the point satisfying both equations. Hence we must solve the system $$\begin{array}{rl}2y& =-x+3,\\ -y& =5x+1.\end{array}$$Adding two times the second equation to the first, we get $2y+2(-y)=-x+3+2(5x+1)$, which simplifies to $0=9x+5$. Solving for $x$, we find that $x=-\frac{5}{9}$. Plugging this into the second equation above, we obtain $-y=5\cdot -\frac{5}{9}+1=-\frac{16}{9}$. So the intersection is $\boxed{\left(-\frac{5}{9},\frac{16}{9}\right)}$.