Jawaban:

To find the solution region, we need to graph the inequalities on a coordinate plane.

First, we'll graph the boundary lines:

4x + 2y = 16 can be simplified to 2x + y = 8 by dividing both sides by 2. We can then find two points on this line by setting x = 0 and y = 8, and x = 4 and y = 0.

5x + 3y = 15 can be simplified to y = (-5/3)x + 5 by subtracting 5x and dividing both sides by 3. We can then find two points on this line by setting x = 0 and y = 5, and x = 3 and y = 0.

Plotting these two lines on a coordinate plane and shading the appropriate regions gives us:

The solution region is the shaded area, which includes all points that satisfy both inequalities. We can see that the region is bounded by the line 4x + 2y = 16 (which is the dotted line), the line 5x + 3y = 15, and the x- and y-axes. The region is also limited to the first quadrant (where x and y are both positive).