1. System of Inequalities
Alg. 2
Mr. Carpenter
BEWARE!!!… QUIZ AFTER

2. System of Inequalities
The ONLY difference between a system of EQUATIONS and a system of INEQUALITIES is that the equations have an “=“ sign and inequalities have “≥, <, >, or ≤.” Which means that…

3. System of Inequalities
Graphing them is almost exactly the same!!!
Steps for graphing:
1st – Solve for Y
-Be sure that you get Y by itself before graphing
2nd – Use “Y = mx + b”
-Start on the Y-axes with “b,” and then, using “m” (which is always attached to the “x”), find your
3rd – Use a dashed/ solid line to graph
- If ≤ or ≥, then you will use a solid line
- If < or >, then you will use a dashed line
4th – Shade on appropriate side of line
- If “Y > line that was graphed” then shade above where the “Y’s” are bigger.
- If “Y < line that was graphed” then shade below where the “Y’s” are smaller.

4. …Let’s try…
We’re going to graph this system of inequalities one at a time
Let’s start with our first inequality…

5. Graphing 1st : Have we solved for y?
2nd: Use “Y = mx +b.” start with “y-intercept” then use “slope”
3rd: Is it a solid or dashed line?
4th: Shade the graph

6. Graphing 1st : Have we solved for y?
2nd: Use “Y = mx +b.” start with “y-intercept” then use “slope”
3rd: Is it a solid or dashed line?
4th: Shade the graph

7. (don’t forget to flip the sign!)
Graphing
1st : Have we solved for y?
2nd: Use “Y = mx +b.” start with “y-intercept” then use “slope”
3rd: Is it a solid or dashed line?
4th: Shade the graph
1st - circle everything that has to do with “y”
2nd – move everything else to other side
3rd – divide by “-2” to get “y” by itself and positive
(don’t forget to flip the sign!)
Graph it!!!

8. Graphing 1st : Have we solved for y?
2nd: Use “Y = mx +b.” start with “y-intercept” then use “slope”
3rd: Is it a solid or dashed line?
4th: Shade the graph
1st - circle everything that has to do with “y”
2nd – move everything else to other side
Graph it!!!

9. Graphing
Where does all of the shading intersect?
That’s our solution!

10. Quick Quiz Question 1
Given “ ,” which is the proper first step to graphing the inequality? a) b) c) d)
E) Please explain this concept

11. Quick Quiz Question 2
When graphing “ ,” which should be my first two steps?
a) Start my line by placing a dot at y = -3 and using the slope to generate all other dots.
b) Start my line by placing a dot at y = 3 and using the slope to generate all other dots.
c) Start my line by placing a dot at y = 2 and using the slope to generate all other dots.
d) Start my line by placing a dot at y = -2 and using the slope to generate all other dots.
E) Please explain this concept

12. Quick Quiz Question 3
When graphing “ ,” what type of line should I use and where should I shade?
a) solid, above
b) solid, below
c) dashed, above
d) dashed, below
e) please explain this concept

13. Making a system using a graph
What pieces of information do you think
are important to re-write the inequalities
in this graph?
Y- intercepts
Slopes
Dashed or Solid Lines
Shading

14. Y- intercepts: y = mx + 5
y = mx + 1
y = mx - 1
Slopes: y = x + 5
y = x + 1
y = x - 1
Lines and Shading: y ≤ x y ≤ x + 1
y ≥ x - 1