1. DRILL: 1. 2.
2x + 4y =1
x - 4y =5
2x – y =6
x + y = 3

2. Using Elimination to Solve a Word Problem:
Two angles are supplementary. The measure of one angle is 10 degrees more than three times the other. Find the measure of each angle.

3. Using Elimination to Solve a Word Problem:
Two angles are supplementary. The measure of one angle is 10 more than three times the other. Find the measure of each angle.
x = degree measure of angle #1
y = degree measure of angle #2
Therefore x + y = 180

4. Using Elimination to Solve a Word Problem:
Two angles are supplementary. The measure of one angle is 10 more than three times the other. Find the measure of each angle.
x + y = 180
x =10 + 3y

5. Using Elimination to Solve a Word Problem:
x + y = 180
x =10 + 3y
x = 180
x =
x = 137.5
(137.5, 42.5)
x + y = 180
-(x - 3y = 10)
4y =170
y = 42.5

7. Using Elimination to Solve a Word Problem:
The sum of two numbers is 70 and their difference is 24. Find the two numbers.

8. Using Elimination to Solve a Word problem:
The sum of two numbers is 70 and their difference is 24. Find the two numbers.
x = first number
y = second number
Therefore, x + y = 70

9. Using Elimination to Solve a Word Problem:
The sum of two numbers is 70 and their difference is 24. Find the two numbers.
x + y = 70
x – y = 24

10. Using Elimination to Solve a Word Problem:
x + y =70
x - y = 24
47 + y = 70
y = 70 – 47
y = 23
2x = 94
x = 47
(47, 23)

11. Now you Try to Solve These Problems Using Elimination.
Find two numbers whose sum is 18 and whose difference is 22.
The sum of two numbers is 128 and their difference is Find the numbers.

12. 3.4 Systems of Linear Inequalities
Objectives:
Write and graph a system of linear inequalities in two variables
Write a system of linear inequalities in two variables for a given solution region

13. Example 1
Graph the system. -8 -6 -4 -2 2 4 6 8

14. Example 1
Graph the system. -8 -6 -4 -2 2 4 6 8

15. Example 2
Graph the system. -8 -6 -4 -2 2 4 6 8

16. Example 2
Graph the system. -8 -6 -4 -2 2 4 6 8

17. Practice
Graph the system. 1)

18. Example 3 Write the system of inequalities graphed below. x < 3-8 -6 -4 -2 2 4 6 8
x < 3
y < 2x + 6

19. Example 4
Graph the linear inequality. -8 -6 -4 -2 2 4 6 8

20. Example 4
Graph the linear inequality. -8 -6 -4 -2 2 4 6 8

21. Example 5
Graph the linear inequality. -8 -6 -4 -2 2 4 6 8

22. Example 5
Graph the linear inequality. -8 -6 -4 -2 2 4 6 8

23. Warm-Up
Solve using substitution.

24. Example 1 Use elimination to solve the system. 8x + 2y = -10
write in standard form
multiply as needed
(-2)
( ) ( )
4x – 3y = 15
(-2)
8x + 2y = -10
-8x + 6y = -30
addition property
8y = -40
8x + 2(-5) = -10
y = -5
8x - 10 = -10
8x = 0
x = 0
(0,-5)

25. Example 2 Use elimination to solve the system. 5x + 3y = 12
write in standard form
multiply as needed
(-1)
( ) ( )
5x + 3y = 15
(-1)
5x + 3y = 12
-5x – 3y = -15
addition property
0 = -3
there is no solution
huh?
the system is inconsistent

26. Example 3 Use elimination to solve the system. 16x – 9y = 8
write in standard form
multiply as needed
(-4)
( ) ( )
4x – 2.25y = 2
(-4)
16x - 9y = 8
-16x + 9y = -8
addition property
0 = 0
consistent, dependent
true
solution is all points on the graph of either equation

27. Practice
Use elimination to solve each system. 1) 2)