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What is the value of x + y + z when 6x + 5y - 2z = -4 and 4x + 5y + 12z = 54?

 Dec 8, 2020
 #1
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We can solve parametrically to get x = 5 - 3t, y = t + 2, and z = 2t + 7.  Then x + y + z = 14.

 Dec 8, 2020
 #2
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6x  +  5y    - 2z =   -4

4x  +  5y   + 12z  = 54

 

We have infinite  soutions for  x, y and z

 

Subtract the  second equation from the  first

 

2x  -14z  =  -58     →  x - 7z =  -29   →  x = -29 + 7z

 

6(-29 + 7z)  + 5y  - 2z =  -4   →   -174 + 42z + 5y  - 2z =  -4  →  5y  + 40z = 170  →  y + 8z  = 34  → y =34 - 8z

 

Letting  z   = 1     x = -22    and y =  26

 

In this case ......x + y +  z  =    5

 

 

cool cool cool

 Dec 8, 2020
 #3
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Add the two equations together to get

10x + 10y + 10z = 50,

and divide by 10.

 Dec 8, 2020

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