# How to graph and solve systems of linear inequalities, using the double-number line?

Oct 9, 2017

Solving system of linear inequalities.
Using a double number-line to solve a system of 2 linear inequalities. (Math article written by Nghi Nguyen)

#### Explanation:

Example 1 . Solve the system:
2x - 3 < 11 (1)
3x > x + 6 (2)
First, solve the 2 inequalities:
Solve (1) --> 2x < 14 --> $x < 7$
On a number-line, draw the solution set:

+++++++++++++0 +++++3++++++++++7------------------

Solve (2) --> 3x - x > 6 --> 2x > 6 --> $x > 3$
Draw the solution set on the second number-line:

----------------------0---------3++++++++++7+++++++++++

By superimposing, we see that the combined solution set of the system is the open interval (3, 7). The 2 end points are not included.
Example 2 . Solve the system:
3x + 7 < x - 1 (1)
2x - 4 > - x + 5 (2)
Solve (1) --> 2x < - 8 -->$x < - 4$
Solve (2) --> 3x > 9 --> $x > 3$

+++++++++++ -4--------------- 0 -------------3----------------------
------------------ -4 -------------------------------3++++++++++++++
By superimposing, we see that the combined solution set are the
open intervals: (-inf. -4) and (3, +inf.)

NOTE. This method can be used to solve a system of 3 linear inequalities.