7.5 System of Inequalities
Objective: Graph the solution to a linear
inequality.
Standard Addressed: 2.8.8.F: Solve and
graph equations and inequalities.

Notice that the form of this inequality is like a
linear equation with the equal sign replaced by an
inequality symbol. Therefore, this inequality is a
linear inequality.

The inequalities that we studied in Chapter 6
were graphed on number lines because they had
just one variable. Inequalities with two
variables are graphed on a coordinate plane.
Graphing Linear Inequalities in 2
Variables

A boundary line divides the coordinate plane into 2 halfplanes. The boundary line can be included in the solution if
the inequality symbol is > or < because these two symbols
contain the equal sign. The shaded area and the boundary
line contain all the ordered pairs that make the inequality
true.

When the inequality symbol is > or <, the points on the
boundary line are included in the solution, and the line is
solid.

When the inequality symbol is > or <, the points on the
boundary line are not included in the solution, and the
line is dashed.
Ex. 1 ** Determine if the given point is
a solution **
ALL OF THE POINTS
ARE SOLUTIONS TO
THE GIVEN
INEQUALITIES!!!
Ex. 2 Graph the following inequalities:

Y > -2x + 3
M = -2
y int (0, 3)
Dashed lined
Shade Above

Y < 1/2x – 2
M=½
y int (0, -2)
Solid Line
Shade Below
Ex. 3 Graph the following
inequalities:
Make sure you solve the inequalities for
slope-intercept form before you graph
them.
 A.
-2y < - x + 4
Y > ½x - 2
M=½
yint (0, -2)
Dotted line / Shaded Above

EX. 3 Graph the following inequalities:
B. 2x – y > -3
-y > -2x – 3
Y < 2x + 3
M=2
Y int (0, 3)
Solid line
Shaded Below

Ex. 3 c.
3y < 2x + 7
y < 2/3x + 7/3
M = 2/3
Y int (0, 7/3)
Dotted line
Shaded below

Ex. 3 d
Y>3
Horizontal Line
Solid line
Shade Above

EX. 3e.
4y + 2x < x – 4
4y < -x – 4
Y < -1/4x -1
M = -1/4
Y int (0, -1)
Solid Line
Shade below

Ex. 3 f.
3x + 18y > o
18y > -3x + 0
Y > -1/6x + 0
M = -1/6
Y int (0, 0)
Solid Line
Shade above
