Método de igualación

►Igualación:

[pic 1]

x= 3- 4y

x= (-5+2y)/3

• 3-4y = (-5+2y)/3

3(3-4y) = -5 +2y

9 - 12y = -5+2y

-12y-2y = -5-9[pic 2]

-14y = -14

y= -14/-14

y= 1

•x+4(1) = 3

x+4 = 3

x = 3-4

x = -1

[pic 3]

x = (13+4y)/3

x = (3-3y)/2

• (13+4y)/3 = (3-3y)/2[pic 4]

2(13+4y) = 3(3-3y)

26+8y = 9-9y

8y+9y = 9-26

17y = -17

y = -17/17

y = -1

•3x-4(-1) = 13

3x+4 = 13

3x = 13-4

3x = 9

x = 9/3

x = 3

[pic 5]

u = 5-v

u = 7+v

• 5-v = 7+v

-v-v = 7-5

-2v = 2

v = 2/-2[pic 6]

v = -1

• u+(-1) = 5

u-1 = 5

u = 5+1

u = 6

[pic 7]

x = -7+2y

x = (-9-3y)/5

• -7+2y = (-9-3y)/5

5(-7+2y) = -9-3y

-35+10y = -9-3y

10y+3y = -9+35

13y = 26

y = 26/13

y = 2

• x-2(2) = -7

x-4 = -7+4

x = -3

[pic 8]

• 4x-3y-3x+7y = 2   → x+4y = 2        

• x+5y-y = 4+2        → x+4y = 6

x = 2-4y

x = 6-4y

• 2-4y = 6-4y

-4y+4y = 6-2

0 = 4 → No existe solución

[pic 9]

p = (7-11q)/5

p = (33-22q)/10

• (7-11q)/5 = (33-22q)/10

10(7-11q) = 5(33-22q) →dividir para 5

2(7-11q) = 33-22q

14-22q = 33-22q

-22q+22q = 33-14

0 = 19 →No hay solución

[pic 10]

4→y = 3-6z-2x

5→(-1) y = -1+4z+x

6→y = (2+2z-3x)/2

•Igualar e. 4 y 5

3-6z-2x = -1+4z+x

-6z-2x-4z-x = -1-3

-10z-3x = -4

-3x = -4+10z

7→x = (-4+10z)/-3

•Igualar e. 5 y 6

-1+4z+x = (2+2z-3x)/2

2(-1+4z+x) = 2+2z-3x

-2+8z+2x = 2+2z-3x

8z+2x-2z+3x = 2+2

6z+5x = 4

5x = 4-6z

8→x = (4-6z)/5

•Igualar e. 7 y 8

(-4+10z)/-3 = (4-6z)/5

5(-4+10z) = -3(4-6z)

-20+50z = -12+18z

50z-18z = -12+20

32z = 8

z = 8/32

z = 1/4 → 0,25

•Reemplazar e. 8

x = (4-6(0,25)/5

x = (4-1,5)/5

x = 2,5/5

x = 1/2 → 0,5

•Reemplazar e. 4

y = 3-6(0,25)-2(0,5)

y = 3-1.5-1

y = 1/2 → 0,5

[pic 11]

4→ x = 10-4y-3z

5→ x = (-2-2y+2z)/4

6→ x = (11+y-z)/3

•Igualar e. 4 y 5

10-4y-3z = (-2-2y+2z)/4

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