Lesson 22-23 - Solving Systems of
Linear Inequalities
The student will be able to:
solve systems of linear inequalities.
CCSS A-REI.5
Prove that, given a system of two equations in two variables, replacing
one equation by the sum of that equation and a multiple of the
other produces a system with the same solutions.
Solving System of Linear Inequalities
So far, we have solved systems using
graphing, tables, substitution, and
elimination.
 Now, instead of equations we are
solving inequalities.
 First let’s remind ourselves on how to
graph inequalities.

1) Graph the inequality
y<x-2
Are these solutions of this inequality?
(-2,3)
(3,-5)
(1,-1)
2) Graph the inequality.
5x – y > 1
Are these solutions of this inequality?
(-2,3)
(3,-5)
(1,4)
3) Now, graph both inequalities on
the same graph.
y < x – 2 5x –
y>1
Are these
solutions of this system?
(-2,3)
(3,-5)
(1,4)
What is another solution?
Solving System of Linear Inequalities
Solving a System of Linear Inequalities
means finding all solutions that are
common to all inequalities in the
system.
 Points have to satisfy both
inequalities.

4) Which are solutions?
x+y>2
2x – y > -5
Ordered Pair
Is it a solution?
Why or Why Not?
(-2,-3)
(3,2)
(3,-1)
(0,5)
Solving a system of linear inequalities.
Step 1: Put the inequalities
in slope intercept form
Step 2: Graph each.
inequality on the same
graph.
Step 3: Identify where both
graphs are shaded.
y = mx + b
Determine solid or dotted line and
which area to shade.
Where shading overlaps (these
points are solutions to BOTH
inequalities)
5) Solve the system by graphing.
x+y>1x
– 3y > 3
2x + 3y > 1
6) Solve the system by graphing.
-x + y > -3
x > -3
x<2
7) Solve the system by graphing.
y>3
y < -1
8) Solve the system by graphing.
x +y>2
2x – y > -5
9) Solve the system by graphing.
y >x–1
y < -2x + 2
10) Solve the system by graphing.
2x + 3y > 6
x – 2y < 4
11) Solve the system by graphing.