Solving Linear Equation: (x,y,z)=(a,a,b)+(c,d,d)

[annoymage]

Homework Statement

(x,y,z)=(a,a,b)+(c,d,d)

to make (a,a,b)+(c,d,d) in terms of x,y,z

Homework Equations

n/a

The Attempt at a Solution

(x,y,z)=(a+c,a+d,b+d)

then

a=c-x=d-y

b=z-d

c=x-a

d=z-b

,,,

there's no free independent variable if i want to use parametric, it only make it tedious T_T,

gimme any clue

 

[annoymage]

hey wait,

can i use like this

a+0b+c+0d=x
a+0b+0c+d=y
0a+b+0c+d=z

try to turn it in row echelon form, let me try first hoho

 

[annoymage]

nop, i still can't find independent variable, help anyone