Question

A system 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

Answer 1

Because the lines are parallel there is not solution.

Answer: 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.