Look at the graph below:
first line joins ordered pairs negative 4, 3 and 2, negative 3. second line joins negative 4, negative 3 and 2, 3. part a shaded above first and second line. part b shaded below first line and above second line. part c shaded below first and second lines. part d shaded above first line and below second line.
which part of the graph best represents the solution set to the system of inequalities y ≤ x + 1 and y + x ≤ −1?
part a
part b
part c
part d

For y =< x + 1,
The line representing the equation is the line joining (-4, -3) and (2, 3) i.e. the second line.
The shaded portion will be the region under the second line.

For y + x =< -1,
The line representing the equation is the line joining (-4, 3) and (2, -3) i.e. the first line.
The shaded portion will be the region under the second line.

The shaded portion common to both lines is the area below the first and the second line.
Therefore, the part of the graph that best represents the solution set to the system of inequalities y ≤ x + 1 and y + x ≤ −1 is part c.