What is the intersection of the lines given by $2y=-x+3$ and $-y=5x+1$?

2y = -x + 3        y = 5x + 1

Rearranging the frst equation we have   x  = 3 - 2y

Sub this into the second equation for x and we have that

y = 5(3-2y) +1

y  =  15 - 10y + 1

11y  = 16

y = 16/11

So

x  =  3 - 2(16/11)

x = 3 - 32/11

x = 33/11 - 32/11  =   1/11

So...the intersection point is  ( 1/11, 16/11)