Question

How many whole number solutions exist to the following system of inequalities?

a) 0
b) 1
c) 2
d) More than 2

Answer 1

The system of inequalities has more than 2 whole number solutions.

Step-by-step explanation:

In order to determine the number of whole number solutions to the given system of inequalities, we need to solve the system first. Let's refer to the given system of inequalities as (1) and (2):

(1) 3x + 2y ≤ 10
(2) 2x - y ≥ 3

For equation (1), the boundary line will be a straight line with a slope of -3/2 passing through the point (0,5). To obtain a valid inequality, we shade the region below this line. For equation (2), the boundary line will be a straight line with a slope of 2 passing through the point (0,-3/2). Here, we shade the region above the line.

The number of whole number solutions can be found by looking at the overlapping region shaded in both inequalities. Counting the lattice points (whole number coordinates) in this region, we find that there is more than 2 whole number solutions.