Download 9 Self-Test Exercises

320
Without graphing, determine whether each of the following
systems of equations has one solution, no solution, or many
solutions:
33. 3x − 2y + 13 = 0
3x + y + 7 = 0
34. 4x + 6y − 14 = 0
2x + 3y − 7 = 0
35. x − 3y + 2 = 0
3x − 9y + 11 = 0
36. 15x + 3y = 10
5x + y = −3
38. 3x − y + 2 = 0
37. 2x − 4y = 6
x − 2y = 3
9x − 3y + 6 = 0
Solve the following systems of equations by using the
Graphical method:
39. y = −2x − 1
y = 3x − 11
40. y = 2x + 3
y = −2x − 1
41. 2x − 3y − 6 = 0
x + 2y − 10 = 0
42. 3x + 4y − 5 = 0
2x − y + 4 = 0
43. 2y = x
y = −x + 3
44. 3y = 2x
y = −3x + 11
45. x + 4y = 8
2x + 5y = 13
46. x + y = 3
2x − y = 12
47. x + 4y + 12 = 0
9x − 2y − 32 = 0
48. x − y − 1 = 0
2x + 3y − 12 = 0
49. 3x + 2y = 5
y = 2x − 1
50. 4x + 3y = 12
9 − 3x = y
Solve the following systems of equations by using either the
Substitution method or the Elimination method:
57. 0.4x − 0.5y = –0.8
0.3x − 0.2y = 0.1
58. 0.2x − 0.3y = –0.6
0.5x + 0.2y = 2.3
59. 5x – 5y ==-–55
3
2
y
y
xx –
-- === 222
33 44
y
60. x + = 2
4 2
2y
x
+
= 4
3
6
3
61. (2x + 1) – 2(y + 7) = –1
4(x + 5) + 3(y – 1) = 28
62. 2(3x + 2) + 5(2y + 7) = 13
3(x + 1) – 4(y – 1) = –15
63. Find the value of two numbers if their sum is 95 and
the difference between the larger number and the
smaller number is 35.
64. Find the value of two numbers if their sum is 84 and
the difference between the larger number and the
smaller number is 48.
Solve the following systems of equations by using the
Elimination method:
51. 8x + 7y = 23
7x + 8y = 22
52. 2x + y = 8
3x + 2y = 7
53. 9x − 2y = −32
x + 4y = −12
54. 5x − 2y + 3 = 0
3x − 2y − 1 = 0
55. 4x + 3y = 12
18 − 6x = 2y
56. 2x + y + 2 = 0
6x = 2y
65. 300 tickets were sold for a theatrical performance.
The tickets cost $28 for adults and $15 for kids. If
$7,230 was collected, how many adults and how
many children attended this play?
66. 640 tickets were sold for a soccer game between
Toronto FC and Liverpool FC. The tickets cost
$35 for adults and $20 for students. If $16,250 was
collected from sales, how many adults and students
attended the game?
9 Self-Test Exercises
Answers to all problems are available at the end of the textbook.
1. Write the following equations in the form
Ax + By = C:
5. Graph the equation 2x − 3y = 9 using a table of values
with 4 points.
a. y =
2
4
x -–
2
3
2x +
b.6y6-– 2x
+
1
= 00
=
4
2. Three vertices of a rectangle ABCD have the points
A (–3, 4), B (5, 4), and C (5, –1). Find the coordinates
of the 4th vertex and the area of the rectangle.
3. Find the slope and y-intercept of the following lines:
a. 2x – 3y + 6 = 0
b. 3x + 4y – 5 = 0
4. Find the equation of the line, in standard form, that
passes through the points P (–4, 5) and Q (1, 1).
6. Use the slope of the lines to determine whether the
pairs of lines are parallel:
a. 3y = 6x – 9 and 4x − 2y = –6
b. 3y + 4x = 0 and 3x + 4y = 2
7. Write the equation of a line, in standard form, that
is parallel to 3x – 2y + 9 = 0 and that passes through
the point (–6, –3).
(Hint: Parallel lines will have the same slope.)
8. Graph the equation 3y + 4x = 0 using the x-intercept,
y-intercept, and another point on the line.
9. Given the following slopes (m) and y-intercepts (b),
write the equations in standard form:
b. m = 2 , b = –2
a. m =-– 1 , b = –4
2
3
Chapter 9 | Graphs and Systems of Linear Equations
321
10. Graph the line that contains the point (–3, 5) and
that has a slope of –3 .
4
11. Write the equation of a line parallel to 2x + 3y = 6 and
that passes through the point P(–6, –1).
12. Write the equation of the line perpendicular to
5x – y = 4 and that passes through the point P(1, 2).
13. Write the equation of the line passing through the
points P(–3, 5) and Q(5, –1).
14. Write the equation of the line that
passes
through the origin and that is perpendicular
to the line passing through the points
P(–3, 5) and Q(5, –1).
15. Write the equation of the line having an x-intercept
equal to 5 and y-intercept equal to –3.
16. Write the equation of the line passing through the
origin and that is parallel to y = 5x − 1.
Without graphing, determine whether each of the following
systems of equations has one solution, no solution, or many
solutions:
17. 4x + 3y − 16 = 0 and 2x − y + 2 = 0
18. x − 3y + 11 = 0 and 2x − 6y + 4 = 0
19. y = 4x + 8 and 8x − 2y + 8 = 0
Solve the following systems of equations by using the
Graphical method:
20. y = 3x + 6
6x – 2y + 12 = 0
21. 2x + 3y + 4 = 0
3x – y + 7 = 0
Solve the following systems of equations by using the
Substitution method:
22. 2x + 4y + 6 = 0
y – 3x + 9 = 0
23. 3x + y = –8
2x + 3y = 4
Solve the following systems of equations by using the
Elimination method:
24. 6x − 4y + 3 = 0
4x − 6y − 3 = 0
25. 3x + 5y − 19 = 0
5x − 2y + 11 = 0
26. Find the value of two numbers if their sum is 65 and
the difference between the larger number and the
smaller number is 5.
27. In a coin box, there are 3 times as many quarters
(25¢) as dimes (10¢). If the total value of all these
coins is $21.25, how many quarters are there?
28. The cost of admission to a concert was $75 for adults
and $50 for students. If 400 tickets were sold and
$28,125 was collected, how many adult tickets were
sold?
29. Henry works in a computer store and earns $500
a month plus a commission of 10% on the sales he
makes. The relationship between his earnings (y) in
a month and the number of computers he sells (x) is
given by the equation y = 500 + 0.10x.
a. What would his commission be if his earnings are
$14,000 in a month?
b. What would his earnings be if his sales are
$250,000 in a month?
30. The fixed costs (FC) of a factory for the month are
$5,000 and the variable costs (VC) to manufacture
each product are $5. The total costs (TC) for the
month are the sum of the fixed costs and the variable
costs per unit, multiplied by the number of products
produced and sold (x).
The relationship between TC, FC, VC, and x is
expressed by the equation TC = (VC)x + FC.
a. What would be the total cost if 90 products were
sold this month?
b. How many products were sold this month if the
total cost is $11,375?
Self-Test Exercises