How many solutions does the following system of equations have?

Solve the second equation for y. To do this, divide both sides by 2

2y = 5y+8
2y/2 = (5y+8)/2
y = (5y)/2 + 8/2
y = (5/2)y + 4

The slope of this equation is identical to the slope of the first equation. Both slopes are 5/2

However the y intercepts are different. This means we have parallel lines that never cross so there are no solutions. The system is inconsistent.