Simultaneous equations

y=2x-3

 4x-2y=5  

4x-2(2x-3)=5

4x-4x+6=5

6=5

Obviously not correct - there ar no solutions.

Now lets see if we vcan work out why.  

y=2x-3      This is a line and the gradient is 2  and a y intercept of -3

4x-2y=5

-2y=-4x+5

y=2x-(5/2)        This is a line with a gradient of 2 and a y intercept of -5/2

Since these 2 lines have different y intercepts but equal gradients they must be parallel lines.

Parallel lines never cross

therefore they have NO simultaneous solutions.    :)