Download 7.6 Solving Systems of Linear Inequalities

7.6 Solving
Systems of
Linear
Inequalities
Bell Work:
• Check to see if the ordered pairs are a solution
of 2x-3y>-2
• A. (0,0)
• B. (0,1)
• C. (2,-1)
Learning Targets:
• I can solve a system of linear inequalities by
graphing.
• I can use a system of linear inequalities to model
a real-life situation.
Remember How to Sketch the
graph of 6x + 5y ≥ 30…
1. Write in slopeintercept form and
graph:
-6/5x
y ≥
+ 6
This will be a solid line.
2. Test a point. (0,0)
6(0) + 5(0) ≥ 30
0 ≥ 30 Not a
solution.
3. Shade the side that
doesn’t include (0,0).
6
4
2
-6 -4 -2
-2
-4
-6
2 4 6 8
With a linear system, you will be
shading 2 or more inequalities.
Where they cross is the solution to
ALL inequalities.
For example…
y<2
x > -1
y > x-2
The solution is the
intersection of all
three inequalities.
So (0,0) is a
solution but (0,3)
is not.
Steps to Graphing Systems of
Linear Inequalities
1.
2.
3.
Sketch the line that corresponds to each inequality.
Lightly shade the half plane that is the graph of each
linear inequality. (Colored pencils may help you
distinguish the different half planes.)
The graph of the system is the intersection of the
shaded half planes. (If you used colored pencils, it is
the region that has been shaded with EVERY color.)
Practice…
y < -2x + 2
y<x+3
y > -x - 1
Practice…
y<4
y>1
How is the solution of a system of
linear inequalities similar to the
solution of a system of linear
equations?
How is it different?
The solution to a system of linear
inequalities must satisfy each
inequality just as the solution to a
system of linear equations must
satisfy each equation.
The solution to a system of linear
inequalities is usually a region,
whereas a solution to a system of