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what is the solution to this 3 by 3 system of equations
2x-y-z=0
x-2z=1
x+y-5z=3

 Apr 9, 2020
 #1
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2x - y - z = 0      (1)
x -2z = 1  ⇒   x = 1 + 2z      (2)
x + y -5z = 3       (3)

 

Sub  (2)  into (1)  and (3)  for   x    and we  have that

 

2 (1 + 2z) - y - z  =  0  ⇒  -y + 3z =  -2    ( 4)

(1 + 2z) + y  -5z  = 3  ⇒     y - 3z  = 2     (5)

 

If we add  (4) and (5)   we  get  that 0 = 0

 

This means  that we have infinite solutions here  for x,y and  z

 

Using (5)  we  have  that   y = 2 + 3z

 

So....holding  z constant  we  have that

 

(x , y , z)   =   ( 1 + 2z , 2 + 3z , z )

 

 

cool cool cool

 Apr 9, 2020

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