Fri
10/23
Learning Objective:
To remember everything
learned in Chapter 3!
Lesson Hw: Chapter 3 Review WS 1
Rev
Mon
10/26
Learning Objective:
To remember everything
learned in Chapter 3!
Lesson Hw: Chapter 3 Review WS 2
Rev
Tues
Learning Objective:
To remember everything
learned in Chapter 3!
10/27
Lesson
Rev
Hw: Chapter 3 Review WS 3
Tues
Learning Objective:
To remember everything
learned in Chapter 3!
10/27
Lesson
Rev
Hw: Quiz Correction
Algebra II
 To
remember everything in
Chapter 3!
1. –4 = 4y – 2x
– 2y = –x + 12
–4 = 4y – 2x
+2x
+2x
2x – 4 = 4y
4
4
4
y=
1
𝑥
2
−1
– 2y = –x + 12
–2
–2
–2
y=
1
𝑥
2
−6
y=
1
𝑥
2
−1
y=
1
𝑥
2
−6
No Solution
Lines are Parallel & will NEVER cross!
2. –9y – 2x = 81
9y = –2x - 81
–9y – 2x = 81
+ 2x +2x
–9y = 2x + 81
–9
–9
–9
y=
2
− 𝑥
9
−9
9y = – 2x – 81
9
9
9
y=
2
− 𝑥
9
−9
y=
2
− 𝑥
9
−9
y=
2
− 𝑥
9
−9
Infinite
Solutions
SAME line will ALWAYS touch
y = 2𝑥 − 9
y = −3𝑥 − 4
(1, – 7)
y > −3𝑥 + 8
y < −3x − 2
No Overlap
No Solution!
No Shading!!!
y<
1
− 𝑥
2
y<
2
𝑥
3
+1
−6
−7𝑥 + 3𝑦 = −13
6.
4𝑥 + 𝑦 = 2
4x + y = 2
-4x
-4x
y = -4x + 2
- 7x + 3(-4x +2) = -13
- 7x – 12x +6 = -13 4(1) + y = 2
-19x = -19
4+y=2
x=1
y=-2
(1, -2)
(-2)(−4𝑥 − 8𝑦 )= −4 (-2) 8𝑥 + 16𝑦 = 8
7.
−8𝑥 − 16𝑦 = −8
−8𝑥 − 16𝑦 = −8
0=0
Infinite Solutions
Same Line!
(-5)(−3𝑥 + 4𝑦) = −4 (-5) 15𝑥 − 20𝑦 = 20
8.
(4)(7𝑥 + 5𝑦 =
) −5 (4) 28𝑥 + 20𝑦 = −20
43x = 0
x=0
(0, -1)
7(0) + 5y = –5
5y = – 5
y = –1
9.
4𝑥 + 3𝑦 + 5𝑧 = 10
𝑥 + 6𝑦 − 5𝑧 = 14
−6𝑥 − 2𝑦 + 5𝑧 = −25
4x + 3y + 5z = 10
x + 6y – 5z = 14
5x + 9y = 24
x + 6y – 5z = 14
–6x – 2y + 5z = –25
–5x + 4y = –11
9.
5𝑥 + 9𝑦 = 24
−5𝑥 + 4𝑦 = −11
13y = 13
5x + 9(1) = 24
y=1
5x + 9 = 24
5x = 15
x=3
3 + 6(1) – 5z = 14
3 + 6 – 5z = 14
9 – 5z = 14
–5z = 5
(3, 1, -1)
z = –1
2𝑥 + 𝑦 + 3𝑧 = 4
5𝑦 + 3𝑧 = −8 5(-1) + 3z = -8
10.
𝑦 = −1
-5 + 3z = -8
3z = -3
z = -1
2x + (-1) + 3(-1) = 4
2x – 1 – 3 = 4
2x – 4 = 4
(4, -1, -1)
2x = 8 x = 4
11. Find the value of two numbers
if their sum is 22 and their
difference is 6
x + y = 22
14 + y = 22
x–y=6
y=8
2x = 28
x = 14
{8, 14}
12. On the first day of choir ticket sales,
6 adults and 7 student ticket sold for a
total of $154. Choir took in $302 on the
second day be selling 13 adult tickets
and 12 student tickets. Find the price of
an adult and a student ticket.
(-12)( 6x + 7y)= 154 (-12) -72x - 84y =-1848
(7)(13x + 12y)= 302 (7) 91x + 84y = 2114
19x = 266
6(14) + 7y = 154
x = 14
84 + 7y = 154
7y = 70
y = 10
$14 for adult tix
$10 for student tix
13. A stadium has 49,000 seats. Section A
seats are $25, Section B seats are $20, and
Section C seats are $15. The number of seats
in Section A equals the total number of seats
in Section B and C. Suppose the stadium
takes in $1,052,000 from each sold out
event, how may seats does each section hold?
x + y + z = 49000
25x + 20y + 15z = 1052000
x=y+z
13.
𝑥 + 𝑦 + 𝑧 = 49000
0
(20) 𝑥 − 𝑦 − 𝑧 = (20)
25𝑥 + 20𝑦 + 15𝑧 = 1052000
x + y + z = 49000
x–y–z=0
2x = 49000
x = 24,500 20x – 20y – 20z = 0
25x + 20y + 15z = 1052000
45x – 5z = 1052000
13. 45(24500) – 5z = 1052000
1102500 – 5z = 1052000
-5z = -50500
Section A: 24,500
Section B: 14,400
z = 10,100
Section C: 10,100
24500 + y + 10100 = 49000
34600 + y = 49000
y = 14,400