Answer:
(0) no solutions.
Step-by-step explanation:
You are given two inequalities:
[tex]y>3x+9,\\ \\y<3x-1.[/tex]
The signs of both inequalities are > and < (without notion "or equal to"), then the boundary lines should be dotted lines. Each of these dotted lines divides the coordinate plane into two parts. You have to determine which of these parts you have to choose.
Substitute the coordinates of the origin (0,0) into these inequalities:
[tex]0>3\cdot 0+9\Rightarrow 0>9,\\ \\0<3\cdot 0-1\Rightarrow 0<-1.[/tex]
Both results are false inequalities, this means that origin doesn't belong to the shaded region. So you have to choose those parts, that do not contain origin (see attached diagram).
As you can see, shaded regions do not intersect (because lines y=3x+9 and y=3x-1 are parallel), so the system has no solutions.
