Objective

1
Objective

• solve systems of linear inequalities in two
  variables

2
Section 6.7 Graph Linear Inequalities
Remember This???

• Linear Inequalities-

the result of replacing the sign in a linear
equation with an inequality sign.
2x 3y gt 4
y 4x - 3
y ½x 3
7y lt 8x - 16
3
Graphing Linear Inequalities
Remember This???

• Graphing Boundary Lines
• Use a dashed line for lt or gt.
• Use a solid line for or .

4
Graph an Inequality
Remember This???
Graph the inequality y gt 4x - 3.
STEP 2
STEP 3
STEP 1
Graph the equation
Test (0,0) in the original inequality.
Shade the half-plane that contains the point
(0,0), because (0,0) is a solution to the
inequality.
5
Graph an Inequality
Remember This???
Graph the inequality x 3y -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point
(1,0), because (1,0) is a solution to the
inequality.
Graph the equation
Test (1,0) in the original inequality.
6
Graph an Inequality
Remember This???
Graph the inequality y -3.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point
(2,0), because (2,0) is a solution to the
inequality.
Graph the equation
Test (2,0) in the original inequality. Use only
the y-coordinate, because the inequality does not
have a x-variable.
7
Graph an Inequality
Remember This???
Graph the inequality x -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that does not contain the
point (3,0), because (3,0) is not a solution to
the inequality.
Graph the equation
Test (3,0) in the original inequality. Use only
the y-coordinate, because the inequality does not
have a x-variable.
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Section 7.6 Solve Systems of Linear Inequalities

• SYSTEM OF INEQUALITIES-
• consists of two or more linear inequalities in
  the same variables.

x y gt 7
Inequality 1
2x y lt 8
Inequality 2
A solution to a system of inequalities is an
ordered pair (a point) that is a solution to both
linear inequalities.
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Solving a System of Inequalities by Graphing
(1) Graph both inequalities in the same plane.
(2) Find the intersection of the two half-planes. The graph of the system is this intersection.
(3) Check a coordinate by substituting into EACH inequality of the system, to see if the point is a solution for both inequalities.
10
Graph a System of Inequalities
y gt -x 2
Inequality 1
y 3x 6
Inequality 2
Graph both inequalities in the same coordinate
plane. The graph of the system is the
intersection of the two half-planes, which is
shown as the darker shade of blue.
(0,1)
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Graph a System of Inequalities
y lt x 4
Inequality 1
y -x 3
Inequality 2
Graph both inequalities in the same coordinate
plane. The graph of the system is the
intersection of the two half-planes, which is
shown as the darker shade of blue.
(5,0)
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Graph a System of THREE Inequalities
y -1
Inequality 1
Graph all three inequalities in the same
coordinate plane. The graph of the system is the
triangular region, which is shown as the darker
shade of blue.
x gt -2
Inequality 2
x 2y 4
Inequality 3
Check (0,0)
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Graph a System of THREE Inequalities
y -x 2
y gt -x
Inequality 1
Inequality 1
y lt 4
y x 4
Inequality 2
Inequality 2
x lt 3
y lt 5
Inequality 3
Inequality 3
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Write a System of Linear Inequalities
INEQUALITY 2 Another boundary line for the
shaded region has a slope of 2 and a y-intercept
of 1. So, its equation is y 2x 1. Because the
shaded region is above the dashed line, the
inequality is y gt 2x 1.
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Homework
NJASK7 Prep

• Text p. 469, 3-8 all, 10-38 evens