Set 22(Page 57)
- c.The graphs of the lines y= 4 and y= x+ 2
are dashed, so that the inequality signs used in
both of the inequalities comprising the system
are eitheror. Next, note that points in the
shaded region lie above the line y= 4 and
below the line y= x+ 2. This means that the
system of linear inequalities for which the
shaded region is the solution set is given by
y4,yx+ 2. - a.The graphs of the lines y= 5 and x= 2 are
solid, which means that the inequality signs
used in both of the inequalities are either or
. Next, note that points in the shaded region
lie above (or on) the line y= 5 and to the left of
(or on) the line x= 2. Therefore, the system of
linear inequalities for which the shaded region
is the solution set is given byy 5,x 2. - a.First, note that the graphs of the lines y= –x
+ 4 and y= x+ 2 are dashed, which means
that the inequality signs used in both of the
inequalities in the system are eitheror.
Next, note that points in the shaded region lie
below the line y= x+ 2 and below the liney =
- x+ 4. This implies that the system of linear
inequalities for which the shaded region is the
solution set is given byyx+ 2,y–x+ 4.- a.First, the graph of the liney = ^14 xis dashed,
so the corresponding inequality should involve
one of the signsor. The graph ofy= –4x
is solid (so the corresponding inequality should
involve one of the signs or ). Points in the
shaded region lie above the liney = ^14 xand
below the line y= –4x. Therefore, the system
of linear inequalities for which the shaded
region is the solution set is given byy^14 x,
y –4x.
341. d.The slope-intercept form of the line 2y – 3x
= –6 isy = ^32 x– 3. The graphs of this line and
y = 5 – ^52 xare solid, so the inequality signs
used in both of the inequalities are either or
. Points in the shaded region lie above (or
on) the line 2y– 3x= – 6 and above (or on)
the liney = 5 – ^52 x. This means that the system
of linear inequalities for which the shaded
region is the solution set is given by 2y– 3x
–6,y 5 – ^52 x.
342. a.Given that the first inequality does not
include equality, but the second inequality
does, we know that the graph of the line y= 2
is dashed and the graph of the line y= 2x+ 1
is solid. Points that satisfy the inequality y 2
must be above the line y= 2, and those satisfy-
ingy
2 x+ 1 must lie below the line y= 2x+- The intersection of these two regions is given
by the illustration in choice a. - b.The slope-intercept forms of the lines 5y=
8(x+ 5) and 12(5 – x) = 5y are, respectively,
y = ^85 x+ 8 andy = –^152 x+ 12. The graph of
the line y = ^85 x+ 8 is solid (so that the corre-
sponding inequality should involve one of the
signsor). The graph ofy = –^152 x+ 12 is
dashed, so that the corresponding inequality
should involve one of the signsor. Points
in the shaded region lie below (or on) the line
5 y= 8(x+ 5) and below the line 12(5 – x) = 5y.
This implies that the system of linear inequali-
ties for which the shaded region is the solution
set is given by 5y 8(x+ 5), 12(5 – x) 5 y. - d.The graph of the liney = 3xis dashed, so
that the corresponding inequality should
involve one of the signs < or >. The graph ofy
= –5 is solid, so that the corresponding
inequality should involve one of the signs
or. Note that points in the shaded region lie
- The intersection of these two regions is given
ANSWERS & EXPLANATIONS–