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Find the ordered triple $(x,y,z)$ that satisfies the following system: \begin{align*} x-2y&=0\\ y-2z&=0\\ x+z&=5. \end{align*}

 Oct 29, 2017
 #1
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x - 2y  = 0     ⇒  x  = 2y       (1)

y - 2z  = 0    ⇒   y  =  2z  ⇒   y/2  =  z    (2)

x + z  =  5       (3)

 

Put (1)  and (2)  into  (3)

 

2y  +  y/2  =  5     multiply through by 2

 

4y  +  y  =  10

 

5y  =  10       ⇒   y  =  2

 

So   x  =  2y   =   4          and    z  =  y/2  =  1

 

 

cool cool cool

 Oct 29, 2017

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