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

p - 2q = 3

q - 2r = -2 + q

p + r = 9 + p

Guest May 19, 2023

#1**+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**

_{.}

Guest May 19, 2023

#2**0 **

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.

gb1falcon May 19, 2023