Question 1205026: The community center needs at least 5 full-time employees and up to 9 part-time volunteers. They want no more than 12 people. Use x to represent the number of full-time employees, and let y represent the number of part-time volunteers. Represent the solution of a system of linear inequality in the situation.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of full-time employees
y = number of part-time volunteers
x and y are integers
They must be nonnegative so  and 
Given facts- The community center needs at least 5 full-time employees.
- [They need] up to 9 part-time volunteers.
- They want no more than 12 people.
Fact 1 leads to 
Fact 2 leads to 
Fact 3 means 
The system of inequalities would be
Because and , we focus on the upper right quadrant only.
Furthermore, we shade to the right of x = 5 because of
We shade below y = 9 because of
Lastly, shade under  to take care of
The line goes through (0,12) and (12,0)
All of those regions overlap to form a triangle with these corner points
A = (5,0)
B = (5,7)
C = (12,0)
Any point inside this region is a solution to the system. Points on the boundary are also solutions as well. Each boundary line is solid due to the "or equal to".
Desmos graph
https://www.desmos.com/calculator/bjoscdwkhm
An example solution in the shaded region is (8,2) marked in blue.
A non-solution example is (8,6) marked in red.
The entire list of solutions is:
(5,7),
(5,6), (6,6)
(5,5), (6,5), (7,5)
(5,4), (6,4), (7,4), (8,4)
(5,3), (6,3), (7,3), (8,3), (9,3)
(5,2), (6,2), (7,2), (8,2), (9,2), (10,2)
(5,1), (6,1), (7,1), (8,1), (9,1), (10,1), (11,1)
(5,0), (6,0), (7,0), (8,0), (9,0), (10,0), (11,0), (12,0)
There are 36 solution points listed above.
1 in the first row, 2 in the second, 3 in the third, and so on to get 1+2+3+4+5+6+7+8 = 36
If x or y were allowed to be non-integer values, then we'd have infinitely many solutions.
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