IXL - Solve systems of linear and absolute value inequalities by graphing (Algebra 2 practice)

Solve the system of inequalities by graphing.

Select a line to change it between solid and dotted. Select a region to shade it.

Coordinate plane graph with 4 quadrants, x-axis coordinates from -10 to 10, y-axis coordinates from -10 to 10.

ref_doc_title.

Learn with an example

question

Solve the system of inequalities by graphing.

≤

Select a line to change it between solid and dotted. Select a region to shade it.

key idea

The graph of

is a horizontal line. Every

-value

including the y-intercept.

The graph of

≤

is the line and the region below the line. Since the line is included, it should be solid.

The graph of the function

–

is shaped like a V. The vertex is at the point

(

)

The slope to the right of the vertex is

and the slope to the left of the vertex is

–

solution

First inequality

Start with the first inequality,

≤

Graph the boundary line,

First, plot two points that have a

-value

of 3, like

(

)

and

(

)

Second, connect the two points. The inequality uses the symbol ≤, so be sure to draw a solid line.

Third, figure out which region to shade. You could remember that when inequalities start with

< or

≤, you should shade below the line. Or you could try a test point, such as

(

)

Plugging

(

)

into

≤

gives a true statement

(

≤

so you should shade the region that contains

(

)

Each approach tells you to shade the region below the line.

Second inequality

Now deal with the second inequality,

Find

and

Rewrite in the form

–

Rewrite in the form

–

The graph of the equation

–

has a vertex at

(

)

with a slope of 1 to the right of the vertex and a slope of

–

to the left of the vertex. This graph looks like the graph of the parent function

First plot the vertex at

(

)

Then plot points to the right and left of the vertex. Since the slope to the right of the vertex is 1, move up 1 and right 1 to plot a point at

(

)

Since the slope to the left of the vertex is

–

move up 1 and left 1 to plot a point at

(

–

)

Second, draw a ray from the vertex through each of the two points,

(

)

and

(

–

)

The inequality uses the symbol <, so be sure to draw a dotted line.

Third, figure out which region to shade. You could remember that when inequalities start with

< or

≤, you should shade below the rays. Or you could try a test point, such as

(

)

Plugging

(

)

into

gives a true statement

(

so you should shade the region that contains

(

)

Each approach tells you to shade the region below the rays.

Solution

Now you have the graph of each inequality. The solution is where the two regions overlap. It shows all the points for which the system of inequalities is true.

Looking for more? Try these:

Lesson: Systems of linear inequalities

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

F.4Solve systems of linear inequalities by graphing

H.5Graph solutions to two-variable absolute value inequalities

Lesson: Systems of linear inequalities

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!