Solving Systems of Inequalities By Graphing

Eric Hoffman

Algebra II

PLHS

Oct. 2007

Important Skills• Work the following problems as the first

part of your notes. You will be graded on this.

• Graph the following inequalities:

x + y ≤ 3 5y – 4x < -20

• Determine whether the given point satisfies each inequality:

3x + 2y ≤ 10, (2,-1) 4x – 2y > 6, (3,3)

Key Topics

• System of Inequalities: two or more inequalities with the same variables

• Solving a System of Inequalities: to solve a system of inequalities you need to find the ordered pairs that satisfy all the inequalities in the system

What exactly does this mean?? Lets look at

this in a graphical perspective.

Key Topics

• Graph the two inequalities:

• y < 2 – x

• y > x + 4

Remember: to graph

inequalities, graph the

boundary line and shade

The region where these two inequalities “overlap” is the region that contains all the solutions to the system of

inequalities

Key TopicsGraph the following systems of inequalities

to find the region which contains all the possible solutions:

y < 2 – x and y > x + 4

x – 3y > 2 and 2x – y < 4 and 2x + 4y ≥ -7

Key Topics

Finding the vertices of the polygonal region formed by a system of inequalities:

Find where the inequalities intersect.

Key Topics

Couple of different ways to find where the inequalities intersect.

Graphically

Algebraically

Key Topics

• Homework: pg. 126 12 – 32 even

11 problems