In order to graph each equation, we need two points of that equation.
a)
For y = 3x - 3, let's use the points (0, -3) and (1, 0)
For y = -3x + 9, let's use the points (2, 3) and (3, 0)
Graphing the first equation in blue and the second one in green, we have:
We can see that the lines have an intersection point, therefore the system has one solution.
b)
For y = -x + 4 let's use the points (1, 3) and (2, 2)
For y = -(2/3)x + 3 let's use the points (3, 1) and (6, -1)
Graphing the first equation in blue and the second one in green, we have:
We can see that the lines have an intersection point, therefore the system has one solution.
c)
For y = (1/2)x - 3.5 let's use the points (1, -3) and (3, -2)
For y = 3x - 11 let's use the points (3, -2) and (4, 1)
Graphing the first equation in blue and the second one in green, we have:
We can see that the lines have an intersection point, therefore the system has one solution.
d)
For y = (3/4)x - 4 let's use the point (4, -1) and (0, -4)
For y = x - 5 let's use the points (3, -2) and (2, -3)
Graphing the first equation in blue and the second one in green, we have:
We can see that the lines have an intersection point, therefore the system has one solution.