There can be regions of solutions over which inequalities are true. The solution region of given system of inequalities is plotted below.
How are function's surface related to the region?
Suppose that the function in consideration be [tex]y = f(x)[/tex] and it is plotted on the 2-D Cartesian coordinate planes.
Those points which lie on the curve of the function would evaluate [tex]f(x) - y = 0[/tex]
Those points lying above the curve would make [tex]f(x) - y < 0[/tex],
and points lying below the curve would make [tex]f(x) - y > 0[/tex] (since y < f(x) )
For the given case, the symbols used are denoting:
c = amount of coffee measured in pounds
t = amount of tea measured in pounds
The given system of inequalities is:
[tex]6c + 13t \leq 3500\\3.50c + 4t \geq 1900[/tex]
The first inequality is true for region below and on the line [tex]6c + 13t = 3500[/tex]
Similarly, the second inequality is true for region above and on the line [tex]3.50c + 4t = 1900[/tex]
Plotting those lines, and getting the region which is above [tex]3.50c + 4t = 1900[/tex] but below [tex]6c + 13t = 3500[/tex] and on these two's intersection is the area which is common for both inequalities.
For a system's solution, we find points which are commonly satisfying all the statements of that system simultaneously.
The solution of the given system of inequalities is plotted below. (the mid intersection of blue and red overlapping along with that intersection point is the solution of the given system).
Learn more about system of inequalities here:
https://brainly.com/question/16339562
