Algebra 1 Common Core Student Edition, Grade 8-9

Ch eck (3, 0) is in the green region. See if (3, 0) satisfies both inequalities.

y i 2x - 3 <— Write both inequalities. —» 2x + y i 2

0 i 2(3) - 3 Substitute (3, 0) for (x, y). —> 2 ( 3 ) + 0 > 2

0 < 3 <— Simplify. The solution checks. —* 6 > 2

Go t It? 1. What is the graph of the system? y > —x + 5

-3jc + y < - 4

You can combine your knowledge of linear equations with your knowledge of

inequalities to describe a graph using a system of inequalities.

Writing a System of Inequalities From a Graph

What system of inequalities is represented by the graph below?
Have you seen a
problem like this
one before?
Ye s. Yo u w r o t e an
inequality from a graph
in Lesson 6-5. Now you'll
write two inequalities.

Pr o b lem 2

To write a system that is represented by the graph, write an inequality that represents

the yellow region and an inequality that represents the blue region.

The graph shows the intersection of the system y < — + 5 and y > x — 1.

1.

Th e red b o u n d ary l i ne

is y = - ^ x + 5. The region

does not include the line,

only points below. The

inequality isy <~\x + 5.

Th e b l u e b o u n d ary l i ne

isy = x - 1. The region

includes the boundary

line and points above.

Th e i n eq u al i t y i s y > x -

Go t It? 2. a. What system of inequalities is represented by the graph?

b. Reasoning In part (a), is the point where the boundary

lines intersect a solution of the system? Explain.

You can model many real-world situations by writing and graphing systems of linear

inequalities. Some real-world situations involve three or more restrictions, so you must

write a system of at least three inequalities.

C

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