Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p
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
.
+214 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.
