+0

# variables

0
9
2

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
+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
+214
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.

May 19, 2023