Download 9 Review Exercises

319
42. An online music store charges $2 for the first song that you download. For every additional song that you download,
you will be charged only $1.50. Write an equation that shows the relationship between the total revenue (y) and the
number of songs sold (x). If you plot a graph of y vs. x, what are the y-intercept and the slope of the line that would
represent the equation?
43. Viktor invested $25,000, part of it at 5% per annum and the remainder at 4% per annum. If the total interest after one
year was $1,150, how much did he invest at each rate?
44. Two investments were made by Adam, totalling $22,500. Part of it was invested at 6% per annum and the remainder
at 5% per annum. The total interest received after one year was $1,295. Find the amount invested at each rate.
45. There are 130 coins consisting of quarters (25¢) and dimes (10¢). If the coins are worth $27.70, how many quarters
and dimes are there?
46. There are 175 coins consisting of dimes (10¢) and nickels (5¢). The coins are worth $15.00. How many dimes and
nickels are there?
47. The sum of two angles is 180°. One angle is 24° less than three times the other angle. Find the measure of the angles.
48. The sum of two angles is 90°. One angle is 15° more than twice the other angle. Find the measure of the angles.
49. A can of juice contains 15% sugar and another can contains 5% sugar. How many liters of each should be mixed
together to get 10 liters of juice that has 10% sugar?
50. Solution A has 25% acid and solution B has 50% acid. How many liters of a solution A and B should be mixed to get
10 liters of 40% acid?
9 Review Exercises
Answers to odd-numbered problems are available at the end of the textbook.
1. In which quadrant or axis do the following points
lie?
a. A (5, −1)
b. B (−2, 3)
c. C (3, 0)
d. D (4, −2)
e. E (2, 0)
f. F (0, 4)
2. In which quadrant or axis do the following points
lie?
a. A (4, −1)
b. B (−5, 0)
c. C (−2, −7)
d. D (0, −3)
e. E (6, 6)
f. F (5, 4)
3. Plot the following points and join them in the order
of A, B, C, D. Identify the type of quadrilateral and
find its area and perimeter.
a. A (6, −3)
b. B (6, −6)
c. C (−2, −6)
d. D (−2, −3)
4. Plot the following points and join them in the order
of P, Q, R, S. Identify the type of quadrilateral and
find its area and perimeter.
a. P (–2, 4)
b. Q (–8, 4)
c. R (–8, –2)
d. S (–2, –2)
Graph the following equations using a table of values with
four points:
Graph the following equations using the x-intercept,
y-intercept, and another point:
11. 3x − 4y = 12
12. x – 2y = –1
13. x – 2y – 6 = 0
14. 3x + y – 4 = 0
15. y = 4x
16. x = 2y
Graph the following equations using the slope and
y-intercept method:
17. y = 4x + 6
18. y = 5x + 4
19. 3x + 2y – 12 = 0
20. 2x + 3y + 6 = 0
– 11
21. y =-– 3 x 4
1
22. y =-– x – 11
3
Find the equation of the line that passes through the
following points:
23. (3, 2) and (7, 5)
24. (4, 6) and (2, 4)
25. (5, –4) and (–1, 4)
26. (0, –7) and (–6, –1)
27. (1, –2) and (4, 7)
28. (3, –4) and (–1, 4)
29. Write the equation of a line parallel to
3x – 4y = 12 and that passes through the point
P(−2, 3).
30. Write the equation of a line parallel to
2x – 3y = 9 and that passes though the point
P(2, –3).
5. 4x – y = 2
6. 2x + 3y = 12
7. x + y – 4 = 0
8. x + 2y – 4 = 0
31. Write the equation of a line perpendicular to
2y = x + 4 and that passes through the point P(–2, 5).
+22
9. y = 1 x +
2
– 22
10. y =-– 1 x 3
32. Write the equation of a line perpendicular to 3x + 4y + 6 = 0
and that passes through the point P(4, –1).
Review 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