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Find the ordered triple (p,q,r) that satisfies the following system:

p - 2q = 3

q - 2r = -2 + q

p + r = 9 + p

 May 19, 2023
 #1
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+1

 

Find the ordered triple (p,q,r) that satisfies the following system:  

p - 2q = 3  

q - 2r = -2 + q  

p + r = 9 + p  

 

Let's identify the three equations as equations 1, 2, and 3.  

 

p - 2q = 3           (eq 1)  

q - 2r = -2 + q     (eq 2)  

p + r = 9 + p        (eq 3)  

 

by (eq 3)                                              p + r  =  9 + p  

subtract p from both sides                         r  =  9  

 

by (eq 2)                                            q – 2r  =  –2 + q  

subtract q from both sides                      –2r  =  –2  

divide both sides by –2                               r  =  1  

 

If the system is to be actual, then  

r can not be equal to both 9 and 1,  

so there must be something wrong  

with the problem as stated.                      no solution  

.

 May 19, 2023
 #2
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Though what was shown previously leads to a contradiction, I will try to figure out a possible solution anyway. First, take p=3+2q.

Substitute into the third equation: 3+2q+r=12+2q. Nothing we can get here can avoid r=9. Then, using the second equation, we find that 18=2, which is not true. I don't think a solution can be found. Check carefully to make sure you didn't have a typo in typing the system.

 May 19, 2023

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