x+1=2y+2, x-2y=1
3(2x+1)=2y+1, 6x+3=2y+1, 6x-2y=-2, (3x-y=-1)
The above are the given equations rearranged.
Subtract the equations in bold print: 5x=-3 so x=-3/5. y=3x+1=-9/5+1=-4/5.
CHECK
(x+1)/(y+1)=(2/5)/(1/5)=2 OK.
(2x+1)/(2y+1)=(-1/5)/(-3/5)=1/3 OK.