Final answer:
To find the corner points that satisfy all three inequalities, graph the boundary lines for each inequality and find where they intersect to form a closed region. The coordinates of the corner points are the points of intersection. By plugging the coordinates into the inequalities, we find that (2, 3) satisfies all three inequalities.
Step-by-step explanation:
To find the corner points that satisfy all three inequalities, we need to solve the system of inequalities:
8x - 9y <= 13
2x + 7y <= 31
10x - 2y >= -3
To start, let's graph the boundary lines for each inequality:
1. Graph the line 8x - 9y = 13. The slope-intercept form of this line is y = (8/9)x - (13/9).
2. Graph the line 2x + 7y = 31. The slope-intercept form of this line is y = (-2/7)x + (31/7).
3. Graph the line 10x - 2y = -3. The slope-intercept form of this line is y = (10/2)x + (3/2).
The coordinates of the corner points that satisfy all three inequalities are the points where the boundaries intersect and form a closed region.
Now, let's check the answer choices to see which coordinates represent one of the corner points:
A) (3, 1)
B) (5, 4)
C) (2, 3)
D) (1, 5)
By plugging the coordinates into the inequalities, we find that (2, 3) satisfies all three inequalities. Therefore, C) (2, 3) represents one of the corner points.