Question

X-3y +27 - - 3
5X+6 Y - Z = 33
4X-y +32 = 8​

Answer 1

Respuesta:

x = -13/48 , y = 1139/24 y z = 629/48

x-3y +27 = 3 (1)

5x+6y-z = 33 (2)

4x-y +32 = 8​ (3)

Método de Sustitución :

1 ) Despejamos a " y " en (1) :

x+3y+27 = 3

x+3y+27-x = 3-x

3y+27 = 3-x

3y+27-27 = 3-x-27

3y = -24-x

3y/3 = (-24-x)/3

y = (-24-x)/3

2 ) Reemplazamos a " y = (-24-x)/3 '' en la ecuación (3) :

4x-((-24-x)/3) + 32 = 8

3(4x)-(3(-24-x)/3)+32 = 8

12x-(-24-x)+32 = 8

12x+24+x+32 = 8

13x+56 = 8

13x+56-56 = 8-56

13x = -48

13x/13 = -48/13

x = -13/48

3 ) Reemplazamos a " x = -13/48 '' en

la ecuación '' x-3y+27 = 3 '' :

x-3y+27 = 3

(-13/48)-3y+27 = 3

-13/48-3y+27-27 = 3-27

-13/48 -3y = -24

48(-13/48)-48(3y) = 48(-24)

-13-144y = -1152

-13-144y+13 = -1152+13

-144y = -1139

-(-144y) = -(-1139)

144y = 1139

144y/144 = 1139/144

y = 1139/144

4 ) Cambiamos a " x = -13/48 '' y a " y = 1139/144 '' en (2) :

5(-13/48)+6(1139/144)-z = 33

-65/48+1139/24 - z = 33

2213/48 - z = 33 ; 33 = 1584/48

2213/48 - z = 1584/48

-z = (1584-2213)/48

-z = -629/48

-(-z) = -(-629/48)

z = 629/48

Explicación paso a paso: