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!

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

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?