I need with this equation

Question

Write an equation that forms a system of equations with −x + y = −9, so that the system has:

a) no solution

b)infinitely many solutions

c)one solution

Answer 1

-x+y= -10 or any number other than -9 and it has no solution. They're inconsistent, contradictory equations. Graphically they're 2 parallel equations that never intersect.

-2x+2y=-18 has infinitely many solutions. They're linearly dependent, just multiply the 1st by 2 to get the 2nd. Graphically, they're the same line, so their "intersection" is all real points.

-x+2y = -9 has a unique solution, y=0, x=9. They have different slopes, but as straight lines they only intersect at one point, on a graph, in quadrant I, or the border between quadrants I and IV