♥•.•´¨`'°ºoO ♥ Ooº°'´¨`•.•♥Sistemas de Ecuaciones Lineales.♥•.•´¨`'°ºoO ♥ Ooº°'´¨`•.•♥

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 Ec.1
3a + 2b = 16 Ec.2


2a = 10 - 4b
a = 10 - 4b
_______ Ec.3
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