1. Bell Work
Solve the system of equations using elimination. 3x – 4y = 10 3y = 2x - 7

2. 6-8: SYSTEMS OF LINEAR INEQUALITIES
Goal: To use graphing to solve systems of linear inequalities.

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

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

5. Solving Systems of Linear Inequalities
The solution also includes points not on the line, so you need to shade the region of the graph:
above the line for ‘y >’ or ‘y ’.
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:

7. Solving Systems of Linear Inequalities
Example, continued:
Graph each line, make dotted or solid and shade the correct area. a:
dotted
shade above b:
dotted
shade below

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

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

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

11. Assignment
Page 282 (1-19) odd