cristian

35
Resuelve el sistema de ecuaciones por el método de determinantes 7 7X - 5Y = 8 8X + 11 Y = D 7 -5 7 11 - 8 8 11 77 + 40 D = 117 D x 9 -5 9 11 - 144 144 11 99 + 720 D x = 819 D y 7 9 7 144 - 8 8 144 1008 - 72 D y = 936 x = 819 / 117 y = 936 / 117 x = 7 y = 8 5 3X + 10 Y = 3 8X - 5Y = D 3 10 3 -5 - 8 8 -5 -15 - 80 D = -95 D x 45 10 45 -5 - 25 25 -5 -225 - 250 D x = -475 D y 3 45 3 25 - 8 8 25 75 - 360 D y = -285 x = -475 / -95 y = -285 / -95 x = 5 y = 3 1 3X + 7Y = 7 2X - 10 Y = D 3 7 3 -10 - 2 2 -10 -30 - 14 D = -44

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Page 1: Cristian

Resuelve el sistema de ecuaciones por el método de determinantes7 7 X - 5 Y = 98 8 X + 11 Y = 144

D 7 -5 7 11 - 8 -58 11 77 + 40

D = 117

D x 9 -5 9 11 - 144 -5144 11 99 + 720

D x = 819

D y 7 9 7 144 - 8 98 144 1008 - 72

D y = 936x = 819 / 117y = 936 / 117

x = 7y = 8

5 3 X + 10 Y = 453 8 X - 5 Y = 25

D 3 10 3 -5 - 8 108 -5 -15 - 80

D = -95

D x 45 10 45 -5 - 25 1025 -5 -225 - 250

D x = -475

D y 3 45 3 25 - 8 458 25 75 - 360

D y = -285x = -475 / -95y = -285 / -95

x = 5y = 3

1 3 X + 7 Y = 527 2 X - 10 Y = -68

D 3 7 3 -10 - 2 72 -10 -30 - 14

D = -44

D x 52 7 52 -10 - -68 7-68 -10 -520 + 476

Page 2: Cristian

D x = -44

D y 3 52 3 -68 - 2 522 -68 -204 - 104

D y = -308x = -44 / -44y = -308 / -44

x = 1y = 7

Resuelve el sistema de ecuaciones por el método de determinantes2 9 X - 11 Y = 71 6 X - 8 Y = 4

D 9 -11 9 -8 - 6 -116 -8 -72 + 66

D = -6

D x 7 -11 7 -8 - 4 -114 -8 -56 + 44

D x = -12

D y 9 7 9 4 - 6 76 4 36 - 42

D y = -6x = -12 / -6y = -6 / -6

x = 2y = 1

1 7 X + 6 Y = 619 7 X - 4 Y = -29

D 7 6 7 -4 - 7 67 -4 -28 - 42

D = -70

D x 61 6 61 -4 - -29 6-29 -4 -244 + 174

D x = -70

D y 7 61 7 -29 - 7 617 -29 -203 - 427

D y = -630x = -70 / -70y = -630 / -70

x = 1

Page 3: Cristian

y = 911 11 X + 5 Y = 151

6 10 X + 11 Y = 176

D 11 5 11 11 - 10 510 11 121 - 50

D = 71

D x 151 5 151 11 - 176 5176 11 1661 - 880

D x = 781

D y 11 151 11 176 - 10 15110 176 1936 - 1510

D y = 426x = 781 / 71y = 426 / 71

x = 11y = 6

Resuelve el sistema de ecuaciones por el método de determinantes6 7 X + 8 Y = 130

11 2 X + 9 Y = 111

D 7 8 7 9 - 2 82 9 63 - 16

D = 47

D x 130 8 130 9 - 111 8111 9 1170 - 888

D x = 282

D y 7 130 7 111 - 2 1302 111 777 - 260

D y = 517x = 282 / 47y = 517 / 47

x = 6y = 11

8 10 X + 5 Y = 851 3 X - 11 Y = 13

D 10 5 10 -11 - 3 53 -11 -110 - 15

D = -125

D x 85 5 85 -11 - 13 5

Page 4: Cristian

13 -11 -935 - 65D x = -1000

D y 10 85 10 13 - 3 853 13 130 - 255

D y = -125x = -1000 / -125y = -125 / -125

x = 8y = 1

6 3 X - 4 Y = -148 9 X - 6 Y = 6

D 3 -4 3 -6 - 9 -49 -6 -18 + 36

D = 18

D x -14 -4 -14 -6 - 6 -46 -6 84 + 24

D x = 108

D y 3 -14 3 6 - 9 -149 6 18 + 126

D y = 144x = 108 / 18y = 144 / 18

x = 6y = 8

Resuelve el sistema de ecuaciones por el método de determinantes8 4 X - 9 Y = -135 6 X + 5 Y = 73

D 4 -9 4 5 - 6 -96 5 20 + 54

D = 74

D x -13 -9 -13 5 - 73 -973 5 -65 + 657

D x = 592

D y 4 -13 4 73 - 6 -136 73 292 + 78

D y = 370x = 592 / 74y = 370 / 74

Page 5: Cristian

x = 8y = 5

6 4 X + 9 Y = 604 7 X - 6 Y = 18

D 4 9 4 -6 - 7 97 -6 -24 - 63

D = -87

D x 60 9 60 -6 - 18 918 -6 -360 - 162

D x = -522

D y 4 60 4 18 - 7 607 18 72 - 420

D y = -348x = -522 / -87y = -348 / -87

x = 6y = 4

2 7 X - 3 Y = -108 8 X + 7 Y = 72

D 7 -3 7 7 - 8 -38 7 49 + 24

D = 73

D x -10 -3 -10 7 - 72 -372 7 -70 + 216

D x = 146

D y 7 -10 7 72 - 8 -108 72 504 + 80

D y = 584x = 146 / 73y = 584 / 73

x = 2y = 8

Resuelve el sistema de ecuaciones por el método de determinantes2 6 X + 2 Y = 183 9 X - 10 Y = -12

D 6 2 6 -10 - 9 29 -10 -60 - 18

D = -78

Page 6: Cristian

D x 18 2 18 -10 - -12 2-12 -10 -180 + 24

D x = -156

D y 6 18 6 -12 - 9 189 -12 -72 - 162

D y = -234x = -156 / -78y = -234 / -78

x = 2y = 3

4 2 X + 7 Y = 8511 5 X - 11 Y = -101

D 2 7 2 -11 - 5 75 -11 -22 - 35

D = -57

D x 85 7 85 -11 - -101 7-101 -11 -935 + 707

D x = -228

D y 2 85 2 -101 - 5 855 -101 -202 - 425

D y = -627x = -228 / -57y = -627 / -57

x = 4y = 11

4 8 X - 10 Y = 23 11 X - 2 Y = 38

D 8 -10 8 -2 - 11 -1011 -2 -16 + 110

D = 94

D x 2 -10 2 -2 - 38 -1038 -2 -4 + 380

D x = 376

D y 8 2 8 38 - 11 211 38 304 - 22

D y = 282x = 376 / 94y = 282 / 94

Page 7: Cristian

x = 4y = 3

Resuelve el sistema de ecuaciones por el método de determinantes

Page 8: Cristian

16 6 X - 5 Y =3 2 X - 4 Y =

D 6 -5 6 -4 - 22 -4 -24 + 10

D = -14

D x 21 -5 21 -4 - 00 -4 -84 + 0

D x = -84

D y 6 21 6 0 - 22 0 0 - 42

D y = -42x = -84 / -14y = -42 / -14

x = 6y = 3

3 7 X + 9 Y =9 3 X - 11 Y =

D 7 9 7 -11 - 33 -11 -77 - 27

D = -104

D x 102 9 102 -11 - -90-90 -11 -1122 + 810

D x = -312

D y 7 102 7 -90 - 33 -90 -630 - 306

D y = -936x = -312 / -104y = -936 / -104

x = 3y = 9

6 3 X + 10 Y =4 2 X + 7 Y =

D 3 10 3 7 - 22 7 21 - 20

D = 1

D x 58 10 58 7 - 4040 7 406 - 400

Page 9: Cristian

D x = 6

D y 3 58 3 40 - 22 40 120 - 116

D y = 4x = 6 / 1y = 4 / 1

x = 6y = 4

23 3 X + 5 Y =4 4 X - 3 Y =

D 3 5 3 -3 - 44 -3 -9 - 20

D = -29

D x 29 5 29 -3 - 00 -3 -87 + 0

D x = -87

D y 3 29 3 0 - 44 0 0 - 116

D y = -116x = -87 / -29y = -116 / -29

x = 3y = 4

10 6 X - 2 Y =4 6 X - 7 Y =

D 6 -2 6 -7 - 66 -7 -42 + 12

D = -30

D x 52 -2 52 -7 - 3232 -7 -364 + 64

D x = -300

D y 6 52 6 32 - 66 32 192 - 312

D y = -120x = -300 / -30y = -120 / -30

x = 10

Page 10: Cristian

y = 46 5 X - 10 Y =3 3 X + 10 Y =

D 5 -10 5 10 - 33 10 50 + 30

D = 80

D x 0 -10 0 10 - 4848 10 0 + 480

D x = 480

D y 5 0 5 48 - 33 48 240 + 0

D y = 240x = 480 / 80y = 240 / 80

x = 6y = 3

37 5 X - 6 Y =6 3 X + 4 Y =

D 5 -6 5 4 - 33 4 20 + 18

D = 38

D x -1 -6 -1 4 - 4545 4 -4 + 270

D x = 266

D y 5 -1 5 45 - 33 45 225 + 3

D y = 228x = 266 / 38y = 228 / 38

x = 7y = 6

9 2 X + 3 Y =3 8 X + 8 Y =

D 2 3 2 8 - 88 8 16 - 24

D = -8

D x 27 3 27 8 - 96

Page 11: Cristian

96 8 216 - 288D x = -72

D y 2 27 2 96 - 88 96 192 - 216

D y = -24x = -72 / -8y = -24 / -8

x = 9y = 3

8 9 X + 10 Y =11 10 X + 11 Y =

D 9 10 9 11 - 1010 11 99 - 100

D = -1

D x 182 10 182 11 - 201201 11 2002 - 2010

D x = -8

D y 9 182 9 201 - 1010 201 1809 - 1820

D y = -11x = -8 / -1y = -11 / -1

x = 8y = 11

45 2 X + 5 Y =9 6 X + 9 Y =

D 2 5 2 9 - 66 9 18 - 30

D = -12

D x 55 5 55 9 - 111111 9 495 - 555

D x = -60

D y 2 55 2 111 - 66 111 222 - 330

D y = -108x = -60 / -12y = -108 / -12

Page 12: Cristian

x = 5y = 9

5 6 X - 7 Y =10 10 X - 2 Y =

D 6 -7 6 -2 - 1010 -2 -12 + 70

D = 58

D x -40 -7 -40 -2 - 3030 -2 80 + 210

D x = 290

D y 6 -40 6 30 - 1010 30 180 + 400

D y = 580x = 290 / 58y = 580 / 58

x = 5y = 10

1 10 X + 8 Y =11 10 X + 3 Y =

D 10 8 10 3 - 1010 3 30 - 80

D = -50

D x 98 8 98 3 - 4343 3 294 - 344

D x = -50

D y 10 98 10 43 - 1010 43 430 - 980

D y = -550x = -50 / -50y = -550 / -50

x = 1y = 11

54 6 X - 6 Y =5 5 X - 4 Y =

D 6 -6 6 -4 - 55 -4 -24 + 30

D = 6

Page 13: Cristian

D x -6 -6 -6 -4 - 00 -4 24 + 0

D x = 24

D y 6 -6 6 0 - 55 0 0 + 30

D y = 30x = 24 / 6y = 30 / 6

x = 4y = 5

7 4 X - 8 Y =5 6 X - 8 Y =

D 4 -8 4 -8 - 66 -8 -32 + 48

D = 16

D x -12 -8 -12 -8 - 22 -8 96 + 16

D x = 112

D y 4 -12 4 2 - 66 2 8 + 72

D y = 80x = 112 / 16y = 80 / 16

x = 7y = 5

1 4 X + 5 Y =10 7 X + 11 Y =

D 4 5 4 11 - 77 11 44 - 35

D = 9

D x 54 5 54 11 - 117117 11 594 - 585

D x = 9

D y 4 54 4 117 - 77 117 468 - 378

D y = 90x = 9 / 9y = 90 / 9

Page 14: Cristian

x = 1y = 10

6

Page 15: Cristian

Resuelve el sistema de ecuaciones por el método de determinantes21 4 7 X - 5 Y

0 6 8 X + 11 Y

-5 D ( ) ( )( )D =

-5 D x ( ) ( )( )D x =

21 D y ( ) ( )( )D y =

x =y =

x =y =

102 5 3 X + 10 Y-90 5 8 X - 5 Y

9 D ( ) ( )( )D =

9 D x ( ) ( )( )D x =

102 D y ( ) ( )( )D y =

x =y =

x =y =

58 8 3 X + 7 Y40 3 2 X - 10 Y

10 D ( ) ( )( )D =

10 D x ( ) ( )( )

Page 16: Cristian

D x =

58 D y ( ) ( )( )D y =

x =y =

x =y =

Resuelve el sistema de ecuaciones por el método de determinantes29 8 9 X - 11 Y

0 5 6 X - 8 Y

5 D ( ) ( )( )D =

5 D x ( ) ( )( )D x =

29 D y ( ) ( )( )D y =

x =y =

x =y =

52 8 7 X + 6 Y32 7 7 X - 4 Y

-2 D ( ) ( )( )D =

-2 D x ( ) ( )( )D x =

52 D y ( ) ( )( )D y =

x =y =

x =

Page 17: Cristian

y =0 5 11 X + 5 Y

48 8 10 X + 11 Y

-10 D ( ) ( )( )D =

-10 D x ( ) ( )( )D x =

0 D y ( ) ( )( )D y =

x =y =

x =y =

Resuelve el sistema de ecuaciones por el método de determinantes-1 8 7 X + 8 Y45 10 2 X + 9 Y

-6 D ( ) ( )( )D =

-6 D x ( ) ( )( )D x =

-1 D y ( ) ( )( )D y =

x =y =

x =y =

27 11 10 X + 5 Y96 2 3 X - 11 Y

3 D ( ) ( )( )D =

3 D x ( ) ( )

Page 18: Cristian

( )D x =

27 D y ( ) ( )( )D y =

x =y =

x =y =

182 6 3 X - 4 Y201 8 9 X - 6 Y

10 D ( ) ( )( )D =

10 D x ( ) ( )( )D x =

182 D y ( ) ( )( )D y =

x =y =

x =y =

Resuelve el sistema de ecuaciones por el método de determinantes55 9 4 X - 9 Y

111 3 6 X + 5 Y

5 D ( ) ( )( )D =

5 D x ( ) ( )( )D x =

55 D y ( ) ( )( )D y =

x =y =

Page 19: Cristian

x =y =

-40 3 4 X + 9 Y30 6 7 X - 6 Y

-7 D ( ) ( )( )D =

-7 D x ( ) ( )( )D x =

-40 D y ( ) ( )( )D y =

x =y =

x =y =

98 10 7 X - 3 Y43 7 8 X + 7 Y

8 D ( ) ( )( )D =

8 D x ( ) ( )( )D x =

98 D y ( ) ( )( )D y =

x =y =

x =y =

Resuelve el sistema de ecuaciones por el método de determinantes-6 4 6 X + 2 Y0 10 9 X - 10 Y

-6 D ( ) ( )( )D =

Page 20: Cristian

-6 D x ( ) ( )( )D x =

-6 D y ( ) ( )( )D y =

x =y =

x =y =

-12 8 2 X + 7 Y2 2 5 X - 11 Y

-8 D ( ) ( )( )D =

-8 D x ( ) ( )( )D x =

-12 D y ( ) ( )( )D y =

x =y =

x =y =

54 4 8 X - 10 Y117 2 11 X - 2 Y

5 D ( ) ( )( )D =

5 D x ( ) ( )( )D x =

54 D y ( ) ( )( )D y =

x =y =

Page 21: Cristian

x =y =

Resuelve el sistema de ecuaciones por el método de determinantes

Page 22: Cristian

= 9 11 6 X - 5= 144 8 2 X - 4

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 45 10 7 X + 9= 25 6 3 X - 11

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 52 11 3 X + 10= -68 5 2 X + 7

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

Page 23: Cristian

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 7 10 3 X + 5= 4 3 4 X - 3

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 61 2 6 X - 2= -29 9 6 X - 7

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =

Page 24: Cristian

y == 151 3 5 X - 10= 176 11 3 X + 10

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 130 9 5 X - 6= 111 11 3 X + 4

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 85 7 2 X + 3= 13 7 8 X + 8

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )

Page 25: Cristian

( ) ( )D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= -14 10 9 X + 10= 6 9 10 X + 11

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= -13 9 2 X + 5= 73 9 6 X + 9

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

Page 26: Cristian

x =y =

= 60 5 6 X - 7= 18 4 10 X - 2

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= -10 6 10 X + 8= 72 8 10 X + 3

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 18 3 6 X - 6= -12 6 5 X - 4

( ) ( ) D ( ) ( )( ) ( )

D =

Page 27: Cristian

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 85 9 4 X - 8= -101 2 6 X - 8

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

x =y =

= 2 10 4 X + 5= 38 8 7 X + 11

( ) ( ) D ( ) ( )( ) ( )

D =

( ) ( ) D x ( ) ( )( ) ( )

D x =

( ) ( ) D y ( ) ( )( ) ( )

D y =x =y =

Page 28: Cristian

x =y =

Page 29: Cristian

1Y = 21Y = 0

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 102Y = -90

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 58Y = 40

( ) ( )( )

( ) ( )( )

Page 30: Cristian

( ) ( )( )

2Y = 29Y = 0

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 52Y = 32

( ) ( )( )

( ) ( )( )

( ) ( )( )

Page 31: Cristian

Y = 0Y = 48

( ) ( )( )

( ) ( )( )

( ) ( )( )

3Y = -1Y = 45

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 27Y = 96

( ) ( )( )

( ) ( )

Page 32: Cristian

( )

( ) ( )( )

Y = 182Y = 201

( ) ( )( )

( ) ( )( )

( ) ( )( )

4Y = 55Y = 111

( ) ( )( )

( ) ( )( )

( ) ( )( )

Page 33: Cristian

Y = -40Y = 30

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 98Y = 43

( ) ( )( )

( ) ( )( )

( ) ( )( )

5Y = -6Y = 0

( ) ( )( )

Page 34: Cristian

( ) ( )( )

( ) ( )( )

Y = -12Y = 2

( ) ( )( )

( ) ( )( )

( ) ( )( )

Y = 54Y = 117

( ) ( )( )

( ) ( )( )

( ) ( )( )

Page 35: Cristian

6