3.3 Graphing and Solving Systems of Linear Equations

System of linear inequalities:

3x-4y³10

-x+4y<8

A possible solution to this system of inequalities is (5,1). The ordered pair must work for both inequalities for it to be the solution.

Graphing a System of Two Inequalities:

· < or > in an inequality represents a dashed line.

· £ or ³ in an inequality represents a solid line.

· Shade the graph area where both inequalities meet.

· Use a “test point” to know where to shade by plugging in an (x,y) to see if it works.

Ex: y£3x-2

y>-2x+3

· Graph the two inequalities.

· Remember the difference between the > and ³ signs when graphing.

· Also remember to use a “test point” to get the shading right.

Graphing a System of Three Inequalities:

Ex: x³0

y³0

2x+5y£10

· Solve the third inequality for y =

5y£-2x+10

y£-2/5x+2

Practice Problems:

1. Graph the following system of inequalities.

y>-2x-1

y£x+3

2. Graph the system of inequalities.

x£0

y³0

2y-4x£8