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11. Sample answer: x  y  5, y  4x
5.1 Practice A
1. yes
2. no
3. 3, 0
12. Sample answer: x  y  12, 2x  3 y  9
4. 2,  4
5. 2, 6
6.  3, 5
13. Sample answer: x  y   3, 4x  9 y  1
7. 8,  2
8. 0.67, 3.5
b. no; The product of 29  4 is 116, which is
greater than 100.
9. 16 bracelets, 21 necklaces
10. y  4 x  4, y  6 x  6; 5, 24; When x  5,
the rectangles have the same area (24 square units).
5.1 Practice B
1. 0,  2
2.  3, 1
3. 4, 2
4.  2,  3
5.  4, 3
6. 1,  2
7. 1.8, 1.6
14. a. 29 multiple choice, 7 essay
8. 1.5, 3.3
9. 28 pencils, 2 pens
15. a  3, b  4
5.2 Practice B
1. 5,  3
2.  3, 1
3. 9, 5
4.  4, 5
5. 1, 1
6. 0, 7
7. x  y  73, y  2x  10; 21 dogs, 52 cats
8. Sample answer: x  y  8, 2x  5 y   2
9. Sample answer: 3x  y  18, y   x  6
10. a. y  10x  90, y  15x  35
10. Sample answer: x  2, x  3 y  2
11. 28 small lanterns and 12 large lanterns
12. a. 2x  2 y  360
b. x  60, y  120
b. no; The intersection point of the two lines is
11, 200, so you will both have the same amount
of money ($200) in your savings accounts after
11 weeks.
13. a. 2 x  2 y  3  360
b. x  37, y  140
14. Sample answer: equation 1: y  2 x  5,
equation 2: x  y  10
5.2 Practice A
1. Sample answer: Solve either equation for y;
The coefficient is 1.
2. Sample answer: Solve the second equation for x.
The coefficient is 1.
3. Sample answer: Solve the first equation for y;
The coefficient is 1.
4. 2, 6
5. 5, 1
6.  2, 3
7. 10, 2
8. 4, 6
9.  3, 1
10. In Step 1, you must solve for x, not  x;
Step 1:  x  4 y  9;  x   4 y  9;
x  4 y  9; Step 2: 34 y  9  2 y  7;
12 y  27  2 y  7; 10 y   20; y   2
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5.3 Practice A
1. 5, 1
2. 2, 3
3. 4, 3
4.  4, 5
5. 3, 1
6. 2, 3
7.  2, 9
8. 3, 2
9. 13, 3
10. 5, 4
11.  4, 1
12. 3, 0
13. x  $20, y  $1.50
14. 3, 1; Sample answer: elimination; Both equations
have 2x term.
15.  2, 7; Sample answer: substitution; Equation 2 is
already solved for y.
Algebra 1
Answers
A1
Answers
16. 4, 2; Sample answer: elimination; It is not easy
to isolate one variable.
6. infinitely many solutions
7. infinitely many solutions; same slope and same y-
intercept
17. a. 34
b. x  y  2, 11  x  y  45
8. no solution; same slope and different y-intercepts
c. x  16, y  18, so 16 medium T-shirts,
9. one solution; different slopes
18 large T-shirts
d. 5 medium and 5 large; The number of medium
and large shirts already ordered is about the
same.
5.3 Practice B
1. 3, 4
2.  2, 4
3. 3, 2
4. 2, 3
5. 10, 13
6. 1, 1
7. 5, 1
8. 8, 7
9. 4, 5
10. 2, 1
11. 2, 3
12. 6, 4
13. subtracted some terms but added others in step 2;
Step 1
4 x  5 y  10
2x  4 y  9
Step 2
Multiply by  2.
4 x  5 y  10
 4 x  8 y  18
13 y   28
y  
28
13
14. 6, 3; Sample answer: substitution; “x = ”
form; y  2x  5; 2x  y  5;
The lines have the same slope and the same
y-intercept, So, the system has infinitely many
solutions.
11. 2x  10 y  18, 3x  15 y  27; no; Equation 2
is a multiple of equation 1, so there are infinitely
many solutions.
5.4 Practice B
1. B; infinitely many solutions
2. A; one solution
3. C; no solution
4. infinitely many solutions
5. no solution
6. 1,  4
7. no solution
8. no solution
9. infinitely many solutions
10. one solution; different slopes
11. infinitely many solutions; same slope and same
y-intercept
12. infinitely many solutions; same slope and same
y-intercept
equation
3 1
; Sample answer: elimination; can get
 2 2
opposite coefficients
15.  ,
1 
16.  , 1; Sample answer: elimination; can get
2 
opposite coefficients
17. you: 17.5 L; your friend: 12.5 L
5.4 Practice A
1. B; no solution
10. Equation 2 is y  2x  5 in slope-intercept
13. no solution; same slope but different y-intercepts
14. one solution; different slopes
15. infinitely many solutions; same slope and same
y-intercept
16. Sample answer: x  y  3, 2x  2 y  6,
3x  y  1
17. a. Sample answer: a  1
b. Sample answer: a  2
2. A; one solution
3. C; infinitely many solutions
4. no solution
A2
Algebra 1
Answers
5. 0, 7
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