Name ________________________________________ Date __________________ Class __________________
LESSON
8-3
Solving Systems by Elimination
Practice and Problem Solving: D
Solve the systems by elimination. The first one is started for you.
⎧ x + 3 y = 14
1. ⎨
⎩2 x − 3 y = − 8
Add the equations:
x + 3 y = 14
+2 x − 3 y = − 8
Subtract the equations:
2 x + 2y = 4
− ( 3 x + 2y = 7)
0 =6
3x + ____
3x
____
or
=6
−3x − ____ = ____
2
x = _____
−x + ____ = ____
−x = ____
Substitute ____ for x in
÷ _____ ÷ _____
one of the equations:
x + 3y = 14
3x + 4y = 26
+ ___ x −___ y = _____
____
− _____
3y = _______
÷ _____ ÷ _____
one of the equations:
one of the equations:
____
+ 2y = 7
−______
Solution: ( ___, ___ )
x = _____
Substitute _____ for x in
3(____) + 2y = 7
y = _____
x = _____
Substitute ____ for x in
3x + 2y = 7
÷3 ÷3
x + 0 = _____
_____
x = _____
+ 3y = 14
− _____
Multiply the second
equation by 2. Then,
add the equations:
⎧ 3 x + 4 y = 26
⎨2( x − 2y = −8)
⎩
2x + 2y = 4
3 ÷ ____
3
÷ ____
____
⎧3 x + 4 y = 26
3. ⎨
⎩ x − 2y = − 8
⎧2 x + 2 y = 4
2. ⎨
⎩3 x + 2y = 7
− ______
2y = _____
÷ _____ ÷ _____
y = ______
x − 2y = −8
____
− 2y = −8
− _____ − _____
−2y = _____
÷ _____ ÷ _____
y = _____
Solution: (____, ____)
Solution: (____, ____)
Solve each system by elimination.
⎧3 x − 2y = 1
4. ⎨
⎩2 x + 2y = 14
________________________
⎧x + y = 4
5. ⎨
⎩3 x + y = 16
_______________________
⎧3 x + 2y = − 26
6. ⎨
⎩2 x − 6 y = −10
________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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7. b + 3m = 7.25; b + 2m = 6.00;
$3.50/bagel, $1.25/muffin
6. Solve the inequalities 40 − 17n < 0 and
35 − 15n < 0 to find the smallest
integers that make x < 0 and y < 0. n
has to be 3 or greater.
8. 2m + 3s = 25; 3m + 4s = 35;
$7.50/ticket, $3.33/snack
9. Answers may vary, but students should
realize that when the equations are
subtracted, an untrue statement results
(0 = −12), which means that there is no
common solution. A graph of this
system will show two parallel lines.
7. Substitute x = 20 and y = 30 in the
equations to see if an integer results; it
does not in either case.
Practice and Problem Solving: D
1. 2x; 2; 2; x; 2; 2; 2; 2; 6; 2; 6
10. Answers may vary, but students should
realize that when the equations are
subtracted, a true statement results
(0 = 0), which means that there are
many combinations of x and y that make
the equations true statements. A graph
of this system will show only one line,
since both equations have the same
graph.
2. x − 3; x − 3; 4x; 4x; 4; 4; x; 7; 7; 7; 7;
4; 7; 4
3. (3, 12)
4. (2, 0)
5. 50; 75; 60; 50; y = 50x + 75; y = 60x +
50; 2.5; 200
For 2.5 hours both decorators charge
the same amount, $200.
Reteach
Practice and Problem Solving: C
1. (2, 3)
2. (7, 9)
3. (−4, 1)
4. (17, 7)
1. a. 14
b. 2x = 18, or x = 9
c. 9
d. 3
Reading Strategies
e. x = 9, y = 5, and z = −3; (9, 5, −3)
1. (6, 4)
2. (−3, 5)
2. (12, 20,
Success for English Learners
15
).
2
5
3. (0, , 2).
3
1. Substitute the value of x into one of the
equations to find y.
2. Option 1 charges $50 to set up the
service and then $30 each month.
Option 2 charges nothing to set up the
service, but charges $40 each month.
4. (7, 4, 3)
5. (1.5, −2, 0)
Practice and Problem Solving: D
1. 0, 3x, 3, 3, 2, 2, 2, 2, 12, 4; 2, 4
LESSON 8-3
2. 2y; −7; 0y; −3; −3; −1; −1; 3; 3; 3; 9; 9; 9;
−2; 2; 2; −1; 3; −1
Practice and Problem Solving: A/B
1. (10, 2)
2. (2, 0)
3. (6, 2)
3. 2; 4; −16; 5; 10; 5; 10; 5; 5; 2; 2; 2; 2; 2;
−10; −2; −2; 5; 2; 5
4. (3, 4)
⎛ 1 15 ⎞
4. ⎜ , ⎟
⎝2 2 ⎠
5. (6, −2)
6. (−8, −1)
⎛ 33 18 ⎞
5. ⎜ ,
⎟
⎝ 10 50 ⎠
Reteach
1. Addition; (4, −1)
⎛7 5⎞
6. ⎜ , ⎟
⎝2 2⎠
2. Subtraction; (−6, 18)
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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