+0  
 
-2
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5
avatar+130 

Find the ordered triple, (p,q,r)

 

\(\begin{align*} p-2q&=0\\ q-2r&=0\\ p+r&=5. \end{align*}\)

 Jul 2, 2020
 #1
avatar
+1

Add equations: (p - 2q) + (q - 2r) + (p + r) = 0 + 0 + 5 ==> 2p - q - r = 5

Divide first equation by 2: p/2 - q = 0

Subtract equations: 5p/2 - r = 0 == > r = 5p/2

Substitute into third equation: p + 5p/2 = 5 ==> 7p/2 = 5 ==> p = 10/7

First equation: p - 2q = 0 ==> q = p/2 = 5/7

Second equation: q - 2r = 0 ==> r = q/2 = 5/14

 

Solution: (10/7, 5/7, 5/14)

 Jul 2, 2020
 #2
avatar+130 
-4

hmmm it appears to be wrong

Creampuff  Jul 2, 2020
 #3
avatar+21953 
+1

p - 2q  =  0     --->                       p - 2q       =  0

q - 2r  =  0     --->   x 2   --->            2q - 4r  =  0

Add down:                                 p         - 4r  =  0

 

p - 4r  =  0     --->                      p - 4r  =  0

p + r  =  5     --->   x -1   --->    -p  -  r  =  -5

Add down:                                   - 5r  =  -5

                                                        r  =  1

 

p + r  =  5   --->   p + 1  =  5     --->     p  =  4

 

q - 2r  =  0   --->   q - 2(1)  =  0     --->   q  =  2

 Jul 2, 2020
 #4
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0

thank you its very helpful

Guest Jul 2, 2020
 #5
avatar+1130 
+2

we first find that q=2r and substitute p-2q into p-4r where we add p+r to get 2p-3r=5  and we also get that p=2q so p=4r and we get 8r-3r=5 so r=1 and then q=2 and p=4 so the ordered pair is (4,2,1).

 Jul 2, 2020

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