we have that
case a)
y=-3x+8 -------> equation 1
6x+2y=4.5--> 2y=-6x+4.5--> divide by 2 both sides--> y=-3x+2.25--> equation 2
equation 1 and equation 2 are parallel
because the slopes are the same
m=-3
so
the system has no solution
case b)
y=9x+6.25 -----> equation 1
-18x+2y=12.5----> 2y=18x+12.5-----> divide by 2 both sides-----> y=9x+6.25--> equation 2
equation 1 and equation 2 are the same
so
the system has infinite solutions
case c)
y=4.5x-5 -----> equation 1
-3x+2y=6----> equation 2
substitute equation 1 in equation 2
-3x+2*[4.5x-5]=6----> -3x+9x-10=6----> 6x=16----> x=2.67
y=4.5*(2.67)-5-----> y=7
the system has the solution (2.67,7)
case d)
y=3x+9 -----> equation 1
x+8y=12.3-----> equation 2
substitute equation 1 in equation 2
x+8*[3x+9]=12.3----> x+24x+72=12.3----> 25x=12.3-72----> x=-2.39
y=3*(-2.39)+9-----> y=1.84
the system has the solution (-2.39,1.84)
therefore
the answer is
the system A has no solution
