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Hey guys,

 

I would greatly appreciate if any one of you maths geniuses could help me with this simultaneous equation question.

The question itself seems very unusual in that I don't end up getting real values for the variables x, y and z.

 

The question is:

x + 5y + 3z = -1

3x + 17y + 5z = 1

2x + 11y + 4z = 0

 

Again, any kind of help would be greatly appreciated.

 

Thanks.

James.

Guest Mar 29, 2017
 #3
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0

x + 5y + 3z = -1

3x + 17y + 5z = 1

2x + 11y + 4z = 0

 

Multiply the first equation by -3   =  -3x - 15y - 9z  = 3.......add this to the second

 

2y - 4z = 4  →  y - 2z  = 2   (1)

 

Multiply the first equation by -2   =  -2x - 10y-6z = 2.....add this to the third

 

y -2z = 2   (2)

 

Now....since (1)  and (2)  are exactly the same, we will have infinite solutions for this system

 

Holding z constant  and using (2)

 

y   =   2z + 2

 

And using the first equation 

x + 5 (2z + 2) + 5z  = -1

x + 10z + 10 + 5z  =  -1

x + 15z + 10  = -1

x =  -11 - 15z

 

So......one form of the solution is {x, y , z }  =  { -11-15z, 2z + 2, z }

 

 

cool cool cool

CPhill  Mar 29, 2017

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