Apuntes Del 9 De Septiembre Del 2008

Sistemas de Ecuaciones Lineales....

Igualacion.


2a + 4b = 10 Ec. 1
3a - 2b = 16 Ec.2





2a = 10 - 4b

a = 10-4b
________ Ec.3
2

3a = 16 + 2b

a = 16 + 2b
__________ Ec. 4
3


Ec. 3 y Ec. 4

10 - 4b 16 + 2b
________ = _________
2 3


30 -12b = 32 + 4b

-16b = 2

b= -2/16

b= -1/8

b Sustituyendo en a

a= 10 - 4 (-1/8)
_____________
2

a = 10 + 1/2
_______
2

a = 20 + 1 / 2 /2

a = 21/2/2/1

a = 21/4

___________________________________________________________________

Comprobacion Ec.1

2 ( 21/4) + 4 ( -1/8) = 10

42/4 - 4/8 = 10

21/2 - 1/2 = 10

10 = 10

___________________________________________________________________

Comprobacion Ec. 2

3 ( 21/4) - 2 ( -1/8) = 16

63/4 - 2/8 = 16

63/4 + 1/4 = 16

64/4 = 16



_________________________________________________________________

Metodo De Sustitucion.


2a + 4b = 10...... Ec1
3a + 2b = 16 ...... Ec2


2a = 10 - 4b

a = 10 - 4b
_______ ..... Ec3
2


Sust. En Ec2.


3 ( 10-4b / 2) - 2b = 16

30 12b
_____ = ______ - 2b = 16
2 2

15 - 6b - 2b = 16

-8 = 16 - 15

b = 1/-8

b = -1/8


En La Ecuacion 3.

a = 10 - 4 (- 1/8)
___________
2

a = 10 + 1/2
_______
2

a = 21/2

a = 21/4

a = 21/2/2/1

a = 21/4


_____________________________________________________________________

Sistema De Eliminacion.

2a + 4b = 10 Ec. 1
3a - 2b = 16 Ec.2


Eliminacion..

4 ( 3a - 2b = 16 )

12-8b = 64

2 ( 2a + 4b =10 )

4a + 8b = 20


12a - 8b = 64
4a + 8b = 20
__________________
16a = 84

a = 84/16

a = 42/8

a = 21/4


De La Ec 1.

2 ( 21/4 ) + 4b = 10

42/4 + 4b = 10

4b = 10 - 42/4

4b = 10-21/2

a = 21/2/2/1

a = 21/4


4b = 20 - 21
______
2

4b = -1/2

b = -1/2/4/1

b = -1/8

___________________________________________________________________

Metodo De Igualacion.

3x + 2y = 6 Ec.1
x - 3y = 8 Ec.2



2x = 6 - 2y

x = 6-2y/3

x = 8 + 3y

6 - 2y 8 + 3y
_____ = _______
3 1

6 - 2y = 24 + 9y

- 2y - 9y = 24 - 6

-11y = 18

y = -18/11


X = 8 + 3 ( -18/11)

X = 8 - 54/11

X = 54 - 88
_______
11

X = -34/11