⇒To check if the given point (2,-8) is the solution to the system you should have a general knowledge that 2 is the input that is represented by variable x and -8 is the output variable represented by letter y.
⇒Now to check if the point is a solution we will have to check for both cases ....y<x-1 and .....y>-x+2
x=2 and y=-8 in the system y< x-1
LHS=-8
RHS=(2)-1
RHS=1
-8<1
The result is true for the first inequality
for the second system inequality
x=2 and y=-8
LHS=-8
RHS=-(2)+2
RHS=-2+2
RHS=0
-8<0 but in the inequality it is saying that -8>0 which is not true but False
⇒As a conclusion point (2,-8) is not a solution to the system as it does not apply to both the conditions.
⇒The answer is no.