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

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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. 

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