The graph of the system of linear inequalities consists of the shaded region that satisfies all three inequalities.
For the first inequality, x < 3.5, we have a vertical line at x = 3.5, and the shaded region is to the left of this line.
For the second inequality, y > 1, we have a horizontal line at y = 1, and the shaded region is above this line.
For the third inequality, y > -x + 1, we have a diagonal line with a slope of -1 passing through the point (1, 0), and the shaded region is above this line.
The graph is the intersection of all three shaded regions, which forms a triangular region in the first quadrant of the coordinate plane.