determine the number of solutions for the systemsx+y=2 and 2x+2y=8

Answer:The number of solutions of the system is zeroStep-by-step explanation:we havea) [tex]x+y=2[/tex]Isolate the variable y[tex]y=-x+2[/tex] ----> equation AThis is the equation of the line in slope intercept formwhereThe slope is m=-1The y-intercept is b=2b) [tex]2x+2y=8[/tex]Isolate the variable y[tex]2y=-2x+8[/tex][tex]y=-x+4[/tex] ----> equation BThis is the equation of the line in slope intercept formwhereThe slope is m=-1The y-intercept is b=4Remember thatIf two lines are parallel, then their slopes are the sameIn this problem the lines A and B are parallel lines with different y-interceptsoThe lines don't intersectthereforeThe system has no solution