Video Transcript
Which of the points below
belongs to the solution set of the system of linear inequalities represented by
the figure shown? (a) One, three; (b) six, eight;
(c) four, three; or (d) three, six.
It’s important to realize that
we aren’t being asked to find the system of linear inequalities represented by
the figure shown but rather to determine which of four given points lies in
their solution set. From the figure, we can see
that there are essentially three types of linear inequalities that have been
graphed. There are two vertical lines,
and the region between these lines is shaded in red. There are two horizontal lines,
and the region between these lines is shaded in blue. Finally, there is a diagonal
line, and the region below this line is shaded in orange. The region that satisfies each
of these inequalities simultaneously is the intersection of the three shaded
regions, which is the triangle shaded in green.
To determine which of the four
given points lies in the solution set of the system of inequalities, we just
need to plot each of these points on the graph and identify any points that are
inside or on the solid boundaries of this region. When we do this, we find that
the only point that lies in the shaded region and hence belongs in the solution
set of the system of linear inequalities is the point four, three.
