1. 3.3A WRITING A SYSTEM
OF LINEAR INEQUALITIES
Today’s objective:
1. I will graph a system of linear
inequalities.
2. I will write system of linear
inequalities given a graph.

2. Homework Check
Workbook: Section 3.6
1. (-2, 4, 5) 2. (2, 3, -1)
3. (1, 2, 3) 4. Many solutions
Textbook: Page 234
34. (5, -1, 0) 35. (4, 3, 1)
36. (2, -2, -5) 37. (2, 3, -2)
38. (1, 3, 1) 39. (3, -2, 6)

3. Solving Systems of Linear
Inequalities
1. We show the solution to a system of
linear inequalities by graphing
them.
a) This process is easier if we put the
inequalities into Slope-Intercept
Form, y = mx + b.

4. Solving Systems of Linear
Inequalities
2. Graph the line using the y-intercept
& slope.
a) If the inequality is < or >, make
the lines dotted (dashed).
b) If the inequality is < or >, make
the lines solid.

5. Solving Systems of Linear
Inequalities
3. The solution also includes points
not on the line, so you need to
shade the region of the graph:
a) above the line for ‘y >’ or ‘y ≥’.
b) below the line for ‘y <’ or ‘y ≤’.

6. Solving Systems of Linear
Inequalities
Example:
a: 3x + 4y > - 4
b: x + 2y < 2
Put in Slope-Intercept Form:
a) 3x + 4 y > −4 b) x + 2 y < 2
4 y > − 3x − 4 2 y < −x + 2
3 1
y > − x −1 y < − x +1
4 2

7. Solving Systems of Linear
Inequalities
Example, continued:
3 1
a : y > − x −1 b : y < − x +1
4 2
Graph each line, make dotted or solid
and shade the correct area.
a: b:
dotted dotted
shade above shade below

8. Solving Systems of Linear
Inequalities
3
a: 3x + 4y > - 4 a : y > − x −1
4

9. Solving Systems of Linear
Inequalities
3
a: 3x + 4y > - 4 a : y > − x −1
4
b: x + 2y < 2 1
b : y < − x +1
2

10. Solving Systems of Linear
Inequalities
a: 3x + 4y > - 4 The area between the
b: x + 2y < 2 green arrows is the
region of overlap and
thus the solution.