12/11 - System of Inequalities

Do Now

Isolate the “y” variable to determine which graph represents the
equation.show your work.

7

9x -3y < -12

b.

a.

LO: SWBAT graph systems of linear inequalities
indicating whether or not the line is included in
the solution set.

DOL: Given a set of problems, students will
correctly graph systems of linear inequalities in
slope-intercept form in two variables and
determine whether the given points are solutions
to the system in at least 4 of 5 questions.

A.3H: Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

8

Lesson Vocabulary

9

Today you will graph systems of ….

Linear inequalities

10

Drag and Drop

The y- intercept is ​ ​

Placeholder

.

The slope is​ ​

Placeholder

.

The line is ​

Placeholder

.

Shade ​

Placeholder

Drag these tiles and drop them in the correct blank above

dashed

below

solid

above

Drag and Drop

The y- intercept is ​ ​

Placeholder

.

The slope is​ ​

Placeholder

.

The line is ​

Placeholder

.

Shade ​

Placeholder

Drag these tiles and drop them in the correct blank above

above

solid

below

dashed

Graphing a system of inequalities

#1

y < 7x -2

y ≥ x +1

y-int

Slope

Line

Shade

3
2

* Remember you can test a point to determine which side of the boundary line to shade.

(0,-2)
7 rise
1 run

dash

below

(0,1)
3 rise
2 run

solid

above

Let’s Graph!

Fill in the Blanks

The solution to a system of linear inequalities is

Hotspot

Plot the points (4, 9) and (2, 6)

Self check ✓

Is the following ordered pair a solution to the system?

#1

y ≥ x +1

(2,6)

(2,6)

6 < 7 ( 2 ) - 2
6 < 12True

6 ≥ ( 2 ) +1

6 ≥ 4True

3
2

Yes, the purple region represents
solutions to both inequalities.

(4, 9) ?

Yes.

Drag and Drop

The y- intercept is ​ ​

Placeholder

.

The slope is​ ​

Placeholder

.

The line is ​

Placeholder

.

Shade ​

Placeholder

Drag these tiles and drop them in the correct blank above

dashed

below

solid

above

Drag and Drop

The y- intercept is ​ ​

Placeholder

.

The slope is​ ​

Placeholder

.

The line is ​

Placeholder

.

Shade ​

Placeholder

Drag these tiles and drop them in the correct blank above

Solid

above

dashed

below

Fill in the Blanks

Because the system of inequalities do not overlap there is

Multiple Choice

Which graph represents this system of equation?

Multiple Choice

Which point is a solution to the system of inequalities?

• $$\left(-2,0\right)$$

• $$\left(-5,2\right)$$

• $$\left(1,2\right)$$

• $$\left(4,2\right)$$

Multiple Choice

Which graph represents this system of equation?

Multiple Choice

Which point is a solution to the system of inequalities?

• $$\left(3,-2\right)$$

• $$\left(2,0\right)$$

• $$\left(1,2\right)$$

• $$\left(-4,2\right)$$

Demonstration of Learning

DOL: Given a set of
problems, students
will correctly graph
systems of linear
inequalities in
slope-intercept form
in two variables and
determine whether
the given points are
solutions to the
system in at least 4
of 5 questions.

23

Open Ended

How can you determine whether
an ordered pair is a solution of a
system of linear inequalities?