System of Linear Equations In Exercises 37-56, solve the system of linear equations.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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10:05
Done elementary_linear_algebra_8th_edi... O
1.1 Exercises See Calcchat.com for worked-out solutions to odd numbered exercises.
Linear Equations In Exercises 1-6, determine whether Graphical Analysis In Exercises 31-36, complete parts
the equation is linear in the variables r and y.
(a)-(e) for the system of equations.
1. 2x - 3y = 4
2. 3x - 4xy = 0
(a) Use a graphing utility to graph the system.
(b) Use the graph to determine whether the system is
32
3. +
+2-1= 0
4. x +y = 4
consistent or inconsistent.
5. 2 sin x - y = 14
6. (cos 3)x + y = - 16
If the system is consistent, approximate the solution.
(d) Solve the system algebraically.
Parametric Representation In Exercises 7-10, find
a parametric representation of the solution set of the
linear equation.
(e) Compare the solution in part (d) with the
approximation in part (e). What can you conclude?
8. 3x - ly = 9
31. -3x - v =
- 3x - y = 3
32.
4x - Sy = 3
7. 2x – 4y = 0
6x + 2y = 1
- &x + 10y = 14
9. x + y +z =1
33. 2x - 8y = 3
r+ y = 0
34. 9x - 4y = 5
r+ ty = 0
10. 12r, + 24x, - 36x, = 12
Graphical Analysis In Exercises 11-24, graph the
system of linear equations. Solve the system and
interpret your answer.
35.
4x - 8y =9
36. -
14.7x + 2.ly = 1.05
44. Lx - 6.3y = - 3.15
0.8x - 1.6y = 1.8
11. 2x + y = 4
12. x+ 3y = 2
-x + 2y = 3
14. x - ty = 1
-2x + y = -4
System of Linear Equations In Exercises 37-56, solve
the system of linear equations.
37. x, - x = 0
3x, - 2x, - -I
X- y = 2
13. —х + у 1
3x - 3y = 4
38. 3x + 2y = 2
6r + 4y = 14
40. X - 2x, = 0
6x, + 2x, - 0
39. 3u + v = 240
15. 3x - Sy -7
16. -x + 3y = 17
u+ 3v = 240
2x + y = 9
4x + 3y = 7
42. x, + x, - 0
18. x- Sy = 21
6x + Sy = 21
x -1 y +2.
+- 4
41. 9x - 3y = -1
+ y = -
* - 2, y - 1
17. 2x - y = 5
5x - y= 11
4x, + X =0
x +
43.
4 3
= 2
19, 3,y-1
4
2
3
2x - y= 12
X - 2y = 5
x- 3y = 20
21. 0.05x - 0.03y = 0.07
0.07x + 0.02y = 0.16
22. 0.2x - 0.5y = - 27.8
0.3x - 0.4y =
44. + , + I
3
+ 4
68.7
3x, - x- -2
45. 0.02r, - 0.05x, = -0.19
0.03x, + 0.04x, = 0.52
46. 0.05x, - 0.03x, = 0.21
0.07x, + 0.02xr, = 0.17
47. х — у -г 0
x + 2y -=6
-z= 5
x + y+ z= 2
-x + 3y + 22 = 8
= 4
2r
24.
363
4x + y = 4
y
23. += 1
4 6
x- y= 3
Back-Substitution In Exercises 25-30, use back-
substitution to solve the system.
25. x, - x = 2
X, = 3
27. -x + y - z = 0
2y + = 3
k = 0
29. 5x, + 2x, + x, = 0
2x, + X
26. 2x, - 4x, = 6
3x, = 9
2x
28. x- y
48.
3y + z= 11
42 = 8
4x + v
30. x, + x, + x,-0
49. 3x, - 2x, + 4x,-1
X + X - 2x, = 3
2r, - 3x, + 6x, = 8
= 0
= 0
The symbol A indicates an exercise in which you are instructed to use a
graphing utility or software program.
Copnge Cnp Lang ARe Runed Mayhepid ad vepat Dda d puny o epde ndiCup
ndhad d
ngpat Cnp Langn d
gh p
1.1 Exercises
50. 5x, - 3x, + 2x, = 3
2x, + 4x - X3 = 7
X - I lx, + 4x, = 3
51. 2r, + X - 3x, =
4x,
- 2r, + 3x, - 13x,- -8
52. X
4x, - 2x, + x, =
2r. - 2r. = 7r. = = 19
Number of Solutions In Exercises 63-66, stati
the system of equations must have at least one sol
Then solve the system and determine whether
exactly one solution or infinitely many solutions.
= 0
63. 4x + 3y + 17; = 0
5x + 4y + 22; = 0
4x + 2y + 19z = 0
65. 5x + 5y - z = 0
10x + 5y + 2z = 0
64. 2x + 3y
4x + 3y - z = 0
&x + 3y + 32 = 0
+ 2r, = 10
+ 4x, =
13
66. 16x + 3y +-0
16x + 2y - z =0
Transcribed Image Text:10:05 Done elementary_linear_algebra_8th_edi... O 1.1 Exercises See Calcchat.com for worked-out solutions to odd numbered exercises. Linear Equations In Exercises 1-6, determine whether Graphical Analysis In Exercises 31-36, complete parts the equation is linear in the variables r and y. (a)-(e) for the system of equations. 1. 2x - 3y = 4 2. 3x - 4xy = 0 (a) Use a graphing utility to graph the system. (b) Use the graph to determine whether the system is 32 3. + +2-1= 0 4. x +y = 4 consistent or inconsistent. 5. 2 sin x - y = 14 6. (cos 3)x + y = - 16 If the system is consistent, approximate the solution. (d) Solve the system algebraically. Parametric Representation In Exercises 7-10, find a parametric representation of the solution set of the linear equation. (e) Compare the solution in part (d) with the approximation in part (e). What can you conclude? 8. 3x - ly = 9 31. -3x - v = - 3x - y = 3 32. 4x - Sy = 3 7. 2x – 4y = 0 6x + 2y = 1 - &x + 10y = 14 9. x + y +z =1 33. 2x - 8y = 3 r+ y = 0 34. 9x - 4y = 5 r+ ty = 0 10. 12r, + 24x, - 36x, = 12 Graphical Analysis In Exercises 11-24, graph the system of linear equations. Solve the system and interpret your answer. 35. 4x - 8y =9 36. - 14.7x + 2.ly = 1.05 44. Lx - 6.3y = - 3.15 0.8x - 1.6y = 1.8 11. 2x + y = 4 12. x+ 3y = 2 -x + 2y = 3 14. x - ty = 1 -2x + y = -4 System of Linear Equations In Exercises 37-56, solve the system of linear equations. 37. x, - x = 0 3x, - 2x, - -I X- y = 2 13. —х + у 1 3x - 3y = 4 38. 3x + 2y = 2 6r + 4y = 14 40. X - 2x, = 0 6x, + 2x, - 0 39. 3u + v = 240 15. 3x - Sy -7 16. -x + 3y = 17 u+ 3v = 240 2x + y = 9 4x + 3y = 7 42. x, + x, - 0 18. x- Sy = 21 6x + Sy = 21 x -1 y +2. +- 4 41. 9x - 3y = -1 + y = - * - 2, y - 1 17. 2x - y = 5 5x - y= 11 4x, + X =0 x + 43. 4 3 = 2 19, 3,y-1 4 2 3 2x - y= 12 X - 2y = 5 x- 3y = 20 21. 0.05x - 0.03y = 0.07 0.07x + 0.02y = 0.16 22. 0.2x - 0.5y = - 27.8 0.3x - 0.4y = 44. + , + I 3 + 4 68.7 3x, - x- -2 45. 0.02r, - 0.05x, = -0.19 0.03x, + 0.04x, = 0.52 46. 0.05x, - 0.03x, = 0.21 0.07x, + 0.02xr, = 0.17 47. х — у -г 0 x + 2y -=6 -z= 5 x + y+ z= 2 -x + 3y + 22 = 8 = 4 2r 24. 363 4x + y = 4 y 23. += 1 4 6 x- y= 3 Back-Substitution In Exercises 25-30, use back- substitution to solve the system. 25. x, - x = 2 X, = 3 27. -x + y - z = 0 2y + = 3 k = 0 29. 5x, + 2x, + x, = 0 2x, + X 26. 2x, - 4x, = 6 3x, = 9 2x 28. x- y 48. 3y + z= 11 42 = 8 4x + v 30. x, + x, + x,-0 49. 3x, - 2x, + 4x,-1 X + X - 2x, = 3 2r, - 3x, + 6x, = 8 = 0 = 0 The symbol A indicates an exercise in which you are instructed to use a graphing utility or software program. Copnge Cnp Lang ARe Runed Mayhepid ad vepat Dda d puny o epde ndiCup ndhad d ngpat Cnp Langn d gh p 1.1 Exercises 50. 5x, - 3x, + 2x, = 3 2x, + 4x - X3 = 7 X - I lx, + 4x, = 3 51. 2r, + X - 3x, = 4x, - 2r, + 3x, - 13x,- -8 52. X 4x, - 2x, + x, = 2r. - 2r. = 7r. = = 19 Number of Solutions In Exercises 63-66, stati the system of equations must have at least one sol Then solve the system and determine whether exactly one solution or infinitely many solutions. = 0 63. 4x + 3y + 17; = 0 5x + 4y + 22; = 0 4x + 2y + 19z = 0 65. 5x + 5y - z = 0 10x + 5y + 2z = 0 64. 2x + 3y 4x + 3y - z = 0 &x + 3y + 32 = 0 + 2r, = 10 + 4x, = 13 66. 16x + 3y +-0 16x + 2y - z =0
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