SOLUTION: if {{{(bx - ay)/b = (cy - bz)/c = (az - cx)/a}}} and given that {{{bx!=ay}}} {{{cy!=bz}}} and {{{az!=cx}}}, which of the follwing is true...?? (1){{{a+b=c}}} (2){{{a+b+c=0}}}

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: if {{{(bx - ay)/b = (cy - bz)/c = (az - cx)/a}}} and given that {{{bx!=ay}}} {{{cy!=bz}}} and {{{az!=cx}}}, which of the follwing is true...?? (1){{{a+b=c}}} (2){{{a+b+c=0}}}      Log On


   

Question 146472: if %28bx+-+ay%29%2Fb+=+%28cy+-+bz%29%2Fc+=+%28az+-+cx%29%2Fa and given that bx%21=ay
cy%21=bz and az%21=cx, which of the follwing is true...??
(1)a%2Bb=c (2)a%2Bb%2Bc=0 (3)ab%2Bbc%2Bca=0 (4)ab%2Bbc-ca=0
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
if %28bx+-+ay%29%2Fb+=+%28cy+-+bz%29%2Fc+=+%28az+-+cx%29%2Fa and given that bx%21=ay
cy%21=bz and az%21=cx, which of the follwing is true...??
(1)a%2Bb=c (2)a%2Bb%2Bc=0 (3)ab%2Bbc%2Bca=0 (4)ab%2Bbc-ca=0

None of those are true necessarily.

Here is a counter-example which shows that:

a=x=2, b=y=1, c=z=1

We show that in this case:

%28bx+-+ay%29%2Fb+=+%28cy+-+bz%29%2Fc+=+%28az+-+cx%29%2Fa

is true by substituting:

%281%2A2+-+2%2A1%29%2F1+=+%281%2A1+-+1%2A1%29%2F1+=+%282%2A1+-+1%2A2%29%2F2

0=0=0

Now we show that

bx%21=ay is true by substituting:

1%2A2%21=2%2A1%21

2=2

Then we show that

cy%21=bz is true by substituting:

1%2A1%21=1%2A1%21

1=1

And finally we show that

az%21=cx is true by substituting:

2%2A1%21=1%2A2%21

2=2

Now look at the four choices:

choice (1)  a%2Bb=c   

Substituting:  2%2B1=1 which is false

choice (2)  a%2Bb%2Bc=0 

Substituting:  2%2B1%2B1=0 which is false

choice (3)  ab%2Bbc%2Bca=0  

Substituting: 2%2A1%2B1%2A1%2B1%2A2=0 which is false

choice (4)ab%2Bbc-ca=0

Substituting: 2%2A1%2B1%2A1-1%2A2=0 which is also false.

So you can tell your teacher that this is a bogus problem.

Edwin