6-6 Graph Systems of Linear Inequalities
Name
Date
Solve by graphing: ⎧ 3x 2y 8
⎨
⎩ x 3y 6
Then name two ordered pairs that are solutions and two that are not.
y
Graph the first inequality.
3x 2y 8
3
y 2x 4
3x 2y $ 8
6
Solve the inequality for y.
3
m 2, b 4
4
(2,6)
x 3y . 6
(3,3)
2
This region includes the boundary line
(6,2)
(2,1)
3
y 2 x 4 and all points above it.
2
0
2
x
4
6
2
Graph the second inequality.
The solution of the system of inequalities
consists of coordinates of all ordered pairs in
the area where the shaded regions intersect.
x 3y 6
1
y 3x 2
Solve the inequality for y.
1
m 3, b 2
(2, 1) and (6, 2) are solutions.
(2, 6) and (3, 3) are not solutions.
This region lies below the boundary line
1
y = 3 x 2.
Copyright © by William H. Sadlier, Inc. All rights reserved.
On a separate sheet of paper, graph the system of inequalities. Tell if
the given ordered pair is a solution of the system. Check students’ graphs.
1. ⎧ x 2y 3
⎨
⎩ 3x 4y 12
x 2y . 3
?
1 2(2) . 3
?
1 4 . 3
True: 5 . 3
2. ⎧ 4x y 6
⎨
⎩ x 3y 8
(1, 2)
3x 4y , 12
?
3(1) 4(2) , 12
?
3 8 , 12
True: 11 , 12
4x y , 6
?
8 5 , 6
True: 13 , 6
yes
(2, 5)
x 3y . 8
?
2 15 . 8
True: 13 . 8
yes
4. ⎧ 2x 5y 3
⎨
⎩ 3x 2y 6
2x 5y . 3
?
9.8 25.5 . 3
False: 35.3 . 3
no
3x 2y # 6
?
14.7 10.2 # 6
True: 4.5 # 6
3x 8y $ 7
?
25$7
True: 7 $ 7
3x 2y $ 1
?
30.9 7.6 $ 1
True: 38.5 $ 1
(10.3, 3.8)
2x y , 6
?
20.6 3.8 , 6
False: 16.8 , 6
no
5. ⎧ 3x 8y 7
⎨
⎩ 6x 16y 6
(4.9, 5.1)
3. ⎧ 3x 2y 1
⎨
⎩ 2x y 6
( 23 , 58 )
6x 16y # 6
?
4 10 # 6
True: 6 # 6
yes
Lesson 6-6, pages 162–165.
6. ⎧ 4x 12y 13
⎨
⎩ 8x 6y 0
4x 12y # 13
?
3 10 # 13
True: 13 # 13
( 34 , 56 )
8x 6y # 0
?
6 5 # 0
True: 1 # 0
yes
Chapter 6
153
For More Practice Go To:
On a separate sheet of paper, graph each system of inequalities.
Describe the solution. Check students’ graphs.
y#x6
y . x 10
m 1; b 6
m 1; b 10
solid line
dashed line
shaded below
shaded above
The solutions are all points on the
solid upper line and between the
parallel lines.
10. ⎧ 5.2x 3.6y 3
⎨
⎩ 26x 18y 2
8. ⎧ y x 4
⎨
⎩y x 4
9. ⎧ 0.1x 0.2y 7
⎨
⎩ 3.2x 6.4y 32
y,x4
y$x4
m 1; b 4
m 1; b 4
dashed line
solid line
shaded below
shaded above
The solutions are all points on the
solid lower line and between the
parallel lines.
1
1
y $ 35 x
y $ 5 x
2
2
1
1
m ; b 35
m ; b 5
2
2
solid line
solid line
shaded above
shaded above
The solution is the set of points
on and above the line
0.1x 0.2y 5 7.
11. ⎧⎪ 6 3y 4
⎨5
⎪ y 11
3
⎩2
5
1 13
5 13
y# x
y# x
9
9
9
6
13
5
13
1
m ;b
m ;b
9
6
9
9
solid line
solid line
shaded below
shaded below
The solution is the set of points on and
below the line 5.2x 3.6y 5 3.
y,
1
13
36
12. ⎧⎪ 4 5x 3
⎨3
⎪ x8
5
⎩2
1
y.
7
6
7
13
m 0; b m 0; b 6
36
dashed line
dashed line
shaded below
shaded above
The graphs of the two linear
inequalities do not overlap.
The system has no solution.
2
1
1
x.
10
12
vertical line
vertical line
dashed line
dashed line
shaded left
shaded right
The graphs of the two linear
inequalities do not overlap.
The system has no solution.
x,
Graph each system on grid paper to show all possible solutions.
Then name three ordered pairs that are solutions. Check students’ graphs.
14. Groceries Toothpaste costs $3.50, and
13. Online shopping An online media company
toothbrushes cost $1.25. If Keisha has only
sells customers songs for $1 and TV shows
$12.50 and needs more than three toothbrushes
for $2.50. José wants to spend no more than
or toothpastes, how many of each could she buy?
$15 but wants to buy at least 4 items (songs
Let x number of tubes bought,
and/or shows).
Let x number of songs bought,
y number of shows
bought. Check that students graph
# 15
{xx y2.5y
$4
and name three ordered pairs in the solution set.
Possible solutions: (8, 2), (4, 4), (1, 5)
15. Graph:⎧ 2x y 9
⎨
⎩ 2x 2y 8
Find and describe the solution.
y number of brushes bought.
Check that students graph the system
3.5x 1.25y # 12.5
and name three ordered pairs
xy.3
in the solution set.
Possible solutions: (1, 7), (2, 4), (3, 1)
{
16. Find the x- and y-intercepts
of the equation.
6x 9y 18
Check students’ graphs.
The solution is (5, 1).
consistent and independent
154
Chapter 6
x-intercept: 3
y-intercept: 2
17. Determine whether the
sequence could be
geometric, arithmetic, or
neither. Use a pattern to
write the next three terms.
500, 5, 0.05, 0.0005, . . .
geometric; 0.000005,
0.00000005, 0.0000000005
Copyright © by William H. Sadlier, Inc. All rights reserved.
7. ⎧ y x 6
⎨
⎩ y x 10