Cho x - 2y + 3z = 56.Tìm x,y,z biết: a,x/6 = y/-7 ; x/3 = z/-8 b,3x = -4y = 2z c,2x = -3y ; 7y = -10z

$a$) `x/6 = y/-7 ; x/3 = z/-8`

`⇒ x/6 = y/-7 = z/-16`

`⇒` `x/6 = 2y/-14 = 3z/-48`

`⇒` `{x-2y+3z}/{6+14-48} = {56}/{-28} = -2`

`⇒` $\left\{\begin{matrix}x=-12 & \\ y=14& \\ z=32 & \end{matrix}\right.$

     Vậy `(x;y;z)=(-12;14;32)`

$b$) `3x = -4y = 2z`

`⇔ x/4 = y/-3 = z/6`

`⇒` `x/4 = 2y/-6 = 3z/18`

`⇒` `{x-2y+3x}/{4 + 6 + 18} = {56}/{28} = 2`

`⇒` $\left\{\begin{matrix}x=8 & \\ y=-6& \\ z=12 & \end{matrix}\right.$

          Vậy `(x;y;z)=(8;-6;12)`

$c$) `2x = -3y ; 7y = -10z`

`⇔ x/-3 = y/2; y/-10 = z/7`

`⇔ x/15 = y/-10 = z/7`

`⇒` `x/15 = 2y/-20 = 3z/21`

`⇒ {x-2y+3z}/{15+20+21} = 56/56 = 1`

`⇒` $\left\{\begin{matrix}x=15 & \\ y=-10& \\ z=7 & \end{matrix}\right.$

    Vậy `(x;y;z)=(15;-10;7)`