1. 1. b 2. a 3. a. (6, 20); b. Plug into both equations
4. (2, 12) 5. (-8/3, -19,3) 6. b 7. It is a real world situation
8. a. Substitute to see answers are close; b. Substitute again
9. Advantage: Can see total number of solutions
Disadvantage: Tough to find exact answer
10. a. 0; b. n/a; c. n/a 12. a. 1; b. (2, 4); c. Plug in
14. a. Graph; b. 3 solutions; c. (-3.8, .2), (-1, 3), (.8, 4.8)
16. Graph the two equations; they do not intercept
18. 20. Whole numbers ≥ 21
-1 0 1 2 3 4 5
2
T − 2π r 24. x = 11 or x = -11
22. h =
2π r
21. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6
22. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6
2x + 2 = 6
23. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6
2x + 2 = 6
2x = 4
24. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x=2
25. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2
2x + 2 = 6
2x = 4
x=2
26. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2
2x + 2 = 6 y=2+2
2x = 4
x=2
27. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2
2x + 2 = 6 y=2+2
2x = 4 y=4
x=2
28. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2 x+y=6
2x + 2 = 6 y=2+2
2x = 4 y=4
x=2
29. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2 x+y=6
2x + 2 = 6 y=2+2 2+4=6
2x = 4 y=4
x=2
30. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2 x+y=6
2x + 2 = 6 y=2+2 2+4=6
2x = 4 y=4
x=2 (2, 4)
31. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2 x+y=6
2x + 2 = 6 y=2+2 2+4=6
2x = 4 y=4
x=2 (2, 4)
Always check your answer.
32. Example 1
Solve.
x + y = 6
y = x + 2
x + (x + 2) = 6 y=x+2 x+y=6
2x + 2 = 6 y=2+2 2+4=6
2x = 4 y=4
x=2 (2, 4)
Always check your answer.
You’ll know you’re right.
33. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
34. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
35. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
36. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750
37. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750
S = 2A
38. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750
S = 2A
C = 1/2 A
39. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A
C = 1/2 A
40. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A 7/2 A = 1750
C = 1/2 A
41. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A 7/2 A = 1750
C = 1/2 A A = 500
42. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A 7/2 A = 1750
C = 1/2 A A = 500
S = 1000
43. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A 7/2 A = 1750
C = 1/2 A A = 500
S = 1000
C = 250
44. Example 2
The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many
children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
A + S + C = 1750 A + 2A + 1/2 A = 1750
S = 2A 7/2 A = 1750
C = 1/2 A A = 500
S = 1000 They printed 500 adult tickets, 1000 student
C = 250 tickets, and 250 children’s tickets
71. Example 5
Solve.
y = 2x 2
2
3y = 6x
2 2
3(2x ) = 6x
2 2
6x = 6x
This is always true!
72. Example 5
Solve.
y = 2x 2
2
3y = 6x
2 2
3(2x ) = 6x
2 2
6x = 6x
This is always true!
These are the same graphs.
73. Example 5
Solve.
y = 2x 2
2
3y = 6x
2 2
3(2x ) = 6x
2 2
6x = 6x
This is always true!
These are the same graphs.
Infinitely many solutions on the parabola
79. Homework
p. 289 #1-20, skip 17, 18
“Too many people are thinking of security instead of opportunity. They
seem more afraid of life than death.” - James F. Byrnes