College Algebra 9th txtbk

SECTION 7–1 Systems of Linear Equations 439
Solve the system of equations in Problems 11–46.
11. x y 7 12. x y 2
x y 3 x y 4
13. 3x 2y 12
14. 3x y 2
7x 2y 8
x 2y 10
15. 3u 5v 15 16. m 2n 4
6u 10v 30
2m 4n 8
17. 3x y 2 18. 2x 8y 10
9x 3y 6
8x 32y 40
19. x y 4
20. 3x y 7
x 3y 12
2x 3y 1
21. 4x 3y 26 22. 9x 3y 24
3x 11y 7
11x 2y 1
23. 7m 12n 1 24. 3p 8q 4
5m 3n 7
15p 10q 10
25. y 0.08x
26. 0.2u 0.5v 0.07
y 100 0.04x
0.8u 0.3v 0.79
2
27. 5x 3 2 y 2
28. 5x 2y 8
7
3x 5 4 y 5
2x 3y 10
29. 2.3y 4.1z 14.21 30. 5.4x 4.2y 12.9
10.1y 2.9z 26.15 3.7x 6.4y 4.5
31. 2x 2 32. 2y z 4
x 3y 2 x 3y 2z 9
x 2y 3z 7
y 3
33. 2y z 2 34. x y z 3
4y 2z 1
x 2z 1
x 2y 3z 0
y z 2
35. x 3y 2 36. 4x 3y 1
2y z 1
8x 6y 4
x y z 1
2x 4y 3z 6
37. 2x z 5 38. x 3y z 4
x 3z 6 x 4y 4z 1
4x 2y z 9
2x y 5z 3
39. x y z 1 40. 2x y 3z 7
2x y z 6
x 2y z 3
7x y 5z 15
3x y 2z 2
41. 2a 4b 3c 6 42. 3u 2v 3w 11
a 3b 2c 15 2u 3v 2w 5
a 2b c 9 u 4v w 5
43. 2x 3y 3z 5 44. x 2y z 2
3x 2y 5z 34 2x 3y 2z 3
5x 4y 2z 23
x 5y z 2
45. x 2y z 4 46. x 8y 2z 1
2x 5y 4z 16 x 3y z 1
x y z 4 2x 11y 3z 2
Problems 49 and 50 refer to the system
ax by h
cx dy k
where x and y are variables and a, b, c, d, h, and k are real constants.
49. Solve the system for x and y in terms of the constants a, b, c, d,
h, and k. Clearly state any assumptions you must make about
the constants during the solution process.
50. Discuss the nature of solutions to systems that do not satisfy
the assumptions you made in Problem 49.
APPLICATIONS
51. AIRSPEED It takes a private airplane 8.75 hours to make the
2,100-mile flight from Atlanta to Los Angeles and 5 hours to make the
return trip. Assuming that the wind blows at a constant rate from Los
Angeles to Atlanta, find the airspeed of the plane and the wind rate.
52. AIRSPEED A plane carries enough fuel for 20 hours of flight at
an airspeed of 150 miles per hour. How far can it fly into a 30 mph
headwind and still have enough fuel to return to its starting point?
(This distance is called the point of no return.)
53. RATE–TIME A crew of eight can row 20 kilometers per hour in
still water. The crew rows upstream and then returns to its starting
point in 15 minutes. If the river is flowing at 2 km/h, how far upstream
did the crew row?
54. RATE–TIME It takes a boat 2 hours to travel 20 miles down a
river and 3 hours to return upstream to its starting point. What is the
rate of the current in the river?
55. BUSINESS A company that supplies bulk candy to bakeries
has one batch of chocolate chips that are 50% dark chocolate and
50% milk chocolate. They have another batch that is 80% dark
chocolate and 20% milk chocolate. One of their customers sends
in a rush order for 100 lb of a mix that is 68% dark chocolate.
How many pounds from each batch should be mixed to meet this
order?
56. BUSINESS A jeweler has two bars of gold alloy in stock, one of
12 carats and the other of 18 carats (24-carat gold is pure gold, 12-
12
18
carat is 24 pure, 18-carat gold is 24 pure, and so on). How many
grams of each alloy must be mixed to obtain 10 grams of 14-carat
gold?
In Problems 47 and 48, solve each system for p and q in terms of
x and y. Explain how you could check your solution and then
perform the check.
47. x 2 p 2q 48. x 1 2p q
y 3 p 3q y 4 p q