SECTION 4.5 Solving Systems of Linear Inequalities^281
39.If a plane can travel 440 mph into the wind and
500 mph with the wind, find the speed of the
wind and the speed of the plane in still air.
40.A small plane travels 200 mph with the wind
and 120 mph against it. Find the speed of the
wind and the speed of the plane in still air.Brain Busters Solve each problem.
41.At the beginning of a bicycle ride for charity, Yady Saldarriaga and Dane McGuckian are
30 mi apart. If they leave at the same time and ride in the same direction, Yady overtakes Dane
in 6 hr. If they ride toward each other, they pass each other in 1 hr. What are their rates?
42.Humera Shams left Farmersville in a plane at noon to travel to Exeter. Walter Wooden left
Exeter in his automobile at 2 P.M. to travel to Farmersville. It is 400 mi from Exeter to
Farmersville. If the sum of their rates was 120 mph, and if they crossed paths at 4 P.M.,
find the rate of each.Graph each linear inequality. See Section 3.5.
43.x+y... 4 44.yĆ- 3 x+ 2 45. 3 x+ 2 y 60PREVIEW EXERCISES
OBJECTIVE
1 Solve systems of
linear inequalities
by graphing.
4.5
Solving Systems of Linear InequalitiesWe graphed the solutions of a linear inequality in Section 3.5.For example,
recall that to graph the solutions of
we first graph by finding and plotting a few ordered pairs that satisfy
the equation. Because the points on the line do notsatisfy the inequality, we use a
dashed line. To decide which region includes the points that are solutions, we choose
a test point not on the line.
Original inequality
Let and
FalseThis false result indicates that the solutions are those points on the side of the line
that does notinclude 1 0, 0 2 , as shown in FIGURE 12.
0 7 12
0 + 31027 x= 0 y=0.
?12
x+ 3 y 7 12
x+ 3 y= 12
x+ 3 y 7 12,
We choose
as a test point.1 0, 0 2xy4012(0, 0)x + 3y > 12FIGURE 12Now we use the same techniques to solve systemsof linear inequalities.
440 mph
into wind500 mph
with wind