IXL - Solve systems of linear inequalities by graphing (Precalculus 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.

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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 vertical line. Every

-value

The graph of

is the region to the left of the line. Since the line is not included, it should be dotted.

The graph of

≥

is the line and the region to the right of the line. Since the line is included, it should be solid.

solution

First inequality

Start with the first inequality,

–

Graph the boundary line,

–

First, plot two points that have an

-value

–

(

–

)

and

(

–

)

Second, connect the two points. 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 to the left of the line. Or you could try a test point, such as

(

)

Plugging

(

)

into

–

gives a false statement

(

–

so you should shade the region that does not contain

(

)

Each approach tells you to shade the region to the left of the line.

Second inequality

Now deal with the second inequality,

≥

–

Graph the boundary line,

–

First, plot two points that have an

-value

–

(

–

)

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 to the right of 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 to the right of the line.

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

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Teacher tools

Work it out

Not feeling ready yet? These can help:

F.2Graph a two-variable linear inequality

N.1Solve a system of equations by graphing

Lesson: Systems of linear inequalities

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