Answer:
Two dotted lines, one solid line
Step-by-step explanation:
The graph of the system of inequalities
[tex]\left\{\begin{array}{l}y>12x-5\\y<-4x+1\\y\ge -23x+15\end{array}\right.[/tex]
will have two dotted lines, one solid line.
To plot the solution set to the inequality with signs < or >, we need to plot the dotted line (because the points of this line are not the solutions to the inequality).
To plot the solution set to the inequality with signs ≤ or ≥, we need to plot the solidd line (because the points of this line are  the solutions to the inequality).
The system above has two inequalities with signs < and > and one inequality with sign ≥, so there will be two dotted lines, one solid line.