Question

the solution to a system of linear inequalities is shown below.


part a: determine a solution to this system of inequalities. write your answer as an ordered pair and explain how you know it is a solution

part b: write a system of two linear inequalities that would have the solution shown in the graph

Answer 1

a: A solution to the system of inequalities is any point in the marked area, for example (1,2) or (-5,5).
b: You can see a horizontal line limiting the area parallel to the x axis at y=1. Everything above this line is accepted so your first inequality is y>1
your second line passes through (0,3) and (4,0) everything below this line is accepted
to get the general form of the line you can insert (0,3):
y=kx+b
3=0*k+b
3=b
and (4,0)
0=4*k+3
-3=4k
-3/4=k

so y=(-3/4)k+3
everything with a lower y is accepted so y<(-3/4)k+3

in the end you get:
y<(-3/4)k+3 and y>1
or together in one formula: 1<y<(-3/4)k+3