8x−3=5+4y
Solve for y:
Add 3 to both sides.
8x=4y+8
Divide both sides by 8.
x=1/2y+1
Plug into equation.
8(1/2y+1)-3=5+4y
Distribute.
4+8-3=5+4y
Combine like items.
4=4y
Divide both sides by 4.
y=1
Unfortunately, you made a mistake transitioning from these 2 steps.
8(12y+1)−3=5+4y
4+8−3=5+4y
Upon distributing the 8 to both terms in the parentheses, you forgot to preserve the linear term (the y). Therefore, the line should be:
4y+8−3=5+4y
If you continue solving from here, you will get 0=0, which means that all solutions are valid.