Download Solving Systems by Elimination with Multiplication

Name ________________________________________ Date __________________ Class __________________
LESSON
8-4
Solving Systems by Elimination with Multiplication
Practice and Problem Solving: D
Fill in the blanks to solve each system by elimination with
multiplication. The first one has been started for you.
⎧3 x + 4 y = 26
1. ⎨
⎩ x − 2y = −8
Multiply the second equation by 2. Then, add the equations:
⎧⎪ 3 x + 4 y = 26
⎨
⎪⎩2 ( x − 2y = −8 )
3x +
4y = 26
−16
2
4
+ ______
x − ______
y = ______
______ x +
0 = ______
______ x = ______
÷ ______ ÷ ______
x
= ______
Substitute ______ for x in one of the equations:
x − 2y = − 8
______ − 2y = −8
− ______ − ______
−2y = ______
÷ ______ ÷ ______
y = ______
Solution: (______, ______)
2. Last month, Stephanie spent $57 on 4 allergy shots and 1 office visit.
This month, she spent $9 after 1 office visit and a refund for 2 allergy
shots from her insurance company. How much do an allergy shot and
an office visit cost?
Complete the equations:
4a + 1v = _________
−2a + 1v = _________
Allergy shot: $_________; office visit: $_________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
178
Reading Strategies
8. All of the lines would intersect at
(−1, −2) but would have different slopes
less than +1 and different y-intercepts.
1. The hand towels are the variable to
eliminate. Bath towels: $10; hand
towels: $5
9. (−1, 2)
2. The adult movie ticket is the variable to
eliminate. Adult tickets: $15; child
tickets: $5
10 −11
Answers may vary, but the two systems
should have equations of the form nx +
(n + 1)y = n + 2 and (n + 3)x + (n + 4)
y = (n + 5), where n is an integer;
(−1, 2); (−1, 2).
Success for English Learners
1. The y-variable is eliminated.
−2y + −2y = 0
2. The “2D” in both equations is eliminated,
and you get 2L = 16. The lunch combo
is $8.
Practice and Problem Solving: D
1. 2; 4; −16; 5; 10; 5; 10; 5; 5; 2; 2; 2; 2; 2;
−10; −2; −2; 5; 2; 5
LESSON 8-4
2. 57; 9; 8; 25
Practice and Problem Solving: A/B
Reteach
1. 4; 6
22 ⎞
⎛ 59
1. ⎜ , −
⎟
7 ⎠
⎝ 7
2. 42; 90
3. 24; 60
111 ⎞
⎛
2. ⎜ 69,
⎟
2 ⎠
⎝
29 ⎞
⎛ 17
4. ⎜ , −
⎟
5 ⎠
⎝ 5
5 ⎞
⎛ 135
3. ⎜
,−
⎟
19 ⎠
⎝ 19
⎛ 1 ⎞
5. ⎜ − , 3 ⎟
⎝ 2 ⎠
⎛ 27 119 ⎞
4. ⎜ , −
⎟
10 ⎠
⎝ 10
6. (−4, −1)
7. 2a + 3y = 134; 3a + 2y = 146; $22
Reading Strategies
8. x + y = 19; 0.25x + 0.3y = 5.1; 7 Galas,
12 Granny Smith’s
1. Multiply the first equation by 3 and the
second equation by 5 to get common
coefficients of −15.
Practice and Problem Solving: C
1. (−1, −2)
2. (−1, −2)
⎧4(9 x − 10 y = 7) ⎧36 x − 40 y = 28
2. ⎨
⇒⎨
⎩5(5 x + 8 y = 31) ⎩25 x + 40 y = 155
3. (−1, −2)
3. (1, −3)
4. The numbers are consecutive whole
numbers.
4. (10, −10)
Success for English Learners
1. −3
5. (−1, −2). They follow the pattern.
2. Multiply the first equation by 3 and the
second by −2, or the first by −3 and the
second by 2.
2
4
3
5
x − ; y = x − ; both slopes are
3
3
4
4
close to but less than +1.
6. y =
7. The slopes are getting larger and
approaching positive one.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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