In this section you will learn how to solve and graph systems of inequalities. Inequalities can be difficult, confusing, and hard to do and with the help of this page, you will be a master this type of math problem. Make sure you have graph paper and a ruler near by. The rules and steps on how to go about graphing inequalities are listed below. Enjoy!

Step 1: Solve the equation for y or the letter they give you.
Step 2: Graph the equation like it contained an = sign.
Step 3: If your inequality sign is < or >, then you draw your line solid.
Step 4: If your inequality sign is < or >, then you draw your line dashed.
Step 5: When you have both lines graph, you have to pick a point that isn’t on your line to use as a tester. Normally you use the point (0,0) because it’s the easiest.
Step 6: Then once you have the points, you shade your graph. If your inequality is true then you shade that side of the line. If it is false shade the other side of the line.

Here is an example:
2x+y<4
3x-y>6
Picture_1_13-26-26.png
3x-y>6
-(-y>-3x+6)
y<3x-6
0<-6

2x+y<4
y<-2x+4
0<-1

Here is another example:
y>x+3
y<-1
y>x+3
0>0-3
0>-3

y<-1
0<-1
Here is another example:
x+y<-1
x+y>3
x+y<-1
y<-x-1
0<-1

NO SOLUTION
x+y>3
y>-x+3
y>3
0>3

worksheet:
7-5 Graphing Systems of Inequalities
answers:




Problem 1:
y-x<3
y-x>2
y-x<3
+x +x
y<x+3
0<3
y-x>2
+x +x
y>x+2
0>2
Picture_2.png
Problem 2:
Here’s the graph. Tell me what the system of inequality is.
Picture_3.png
The inequality is:
y>-x and y>x

Problem 3:
y>2 x<-2
0>2 0<-2
Picture_4.png

Helpful Links:

http://www.regentsprep.org/rEGENTS/math/ginequal/PracGr.htm

[[http://www.regentsprep.org/regents/math/ginequal/grineqa.htm