SECTION 4.5 Solving Systems of Linear Inequalities^283
Solving a System of Linear InequalitiesGraph the solution set of the system.
FIGURE 15shows the graphs of both
and Dashed lines show that the
graphs of the inequalities do not include their
boundary lines. Use as a test point to deter-
mine the region to shade for each inequality.
The solution set of the system is the region with
the gray shading. The solution set does not include
either boundary line.
NOW TRYSolving a System of Three Linear InequalitiesGraph the solution set of the system.
Recall that is a vertical line through the
point , and is a horizontal line through
the point. The graph of the solution set is the
shaded region in FIGURE 16, including all boundary
lines. (Here, use as a test point to confirm that
the correct region is shaded.)
1 3, 2 2
1 0, 4 2
1 2, 0 2 y= 4
x= 2
y... 4
xÚ 2
4 x- 3 y... 8
EXAMPLE 3
1 0, 0 2
2 x+ y 6 2.
x-y 7 5
2 x+y 62
x-y 75
EXAMPLE 2
NOW TRYNOTEWe usually do all the work on one set of axes. In the remaining examples,
only one graph is shown. Be sure that the region of the final solution is clearly
indicated.
NOW TRY
EXERCISE 3
Graph the solution set of the
system.
y... 4xÚ- 2x-y 62NOW TRY
EXERCISE 2
Graph the solution set of the
system.
x- 2 y 602 x+ 5 y 710xy2 x + y < 2x – y > 5Solution set02
5–5FIGURE 15xy
2
0 5
2 x + 5y > 10
x – 2y < 0NOW TRY ANSWERS
2.
xy
4–2 (^0) x – y < 2
y ≤ 4
x ≥ –2
We can graph the solution set of the following system with a calculator.
To graph the first inequality, we direct the calculator to shade belowthe line
( because of the symbol).
To graph the second inequality, we direct the calculator to shade abovethe line
( because of the symbol).
FIGURE 17(a)on the next page shows these directions on a TI-83/84 Plus calculator.
Graphing in the standard viewing window gives the screen in FIGURE 17(b).
Y 2 =-2X- 5 7
Y 1 =3X + 2 6
y7- 2 x- 5
y 63 x+ 2
CONNECTIONS
xy4 x – 3y ≤ (^8) x ≥ 2
y ≤ 4
Solution set
0
2
2
FIGURE 16