algebra: unknown variables problem?
Find x,y, and z:
x(x+y+z)=6
y(x+y+z)=12
z(x+y+z)=18
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Find x,y, and z:
x(x+y+z)=6
y(x+y+z)=12
z(x+y+z)=18
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Answers & Comments
(x+y+z)=A
x*A=6 => A=6/x
y*A=12=>A=12/y
z*A=18=>A=18/z
6/x=12/y=18/z
6/x=12/y =>12x=6y =>6y=12x=>y=12x/6=>y=2x
6/x=18/z =>18x=6z =>6z=18x=>z=18x/6=>z=3x
x(x+y+z)=6
x(x+2x+3x)=6
x*6x=6
x^2=1=>x=1 or x=-1
y=2x =>y=2 or y=-2
z=3x =>z=3 or z=-3