Asystem of equations is graphed on the coordinate plane.

y = 1/2x + 4

y = 1/2x + 3

select the number of solutions for the system of equations from the list below

no solution, many solutions, or infinite solutions

Because the lines are parallel there is not solution. 

no solution.

Two lines with the same slope and different y-intercept are parallel, and there is not cut-off point between these line, (there is not solution).
this is a line: y=mx+b
m=slope
b=y-intercept. 

We can check it out our answer solving the system.
y=1/2x+4
y=1/2x+3

We solve by equalization method.

1/2x+4=1/2x+3
1/2 x-1/2x=3-4
0≠-1; and we can see that 0 is different to -1, therefore there is not solution.