+430 Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p
+1908 WAIT A SECOND! Let's note something real quick.
First, let's look at the first equation. We want only two equations, we isolate p in terms of r.
We get that
\(p=3+2q\)
Subsituting this value of p into the second and third equation, we get the system with r and q, we get
\(q-2r=-2+q\\ 3+2q+r=9+3+2q\)
Now, focusing on the first equation of the new system, isolating r, we find that
\(r=1\)
Plugging in this value for r into the second equation, we have that
\(3+2q+1=2q+12\\2q+4=2q+12\\-8=0\)
THIS IS DEFINITELY NOT TRUE.
In conclusion, we know that this system has NO SOLUTIONS.
I think this is right...
Thanks! :)
+1908 WAIT A SECOND! Let's note something real quick.
First, let's look at the first equation. We want only two equations, we isolate p in terms of r.
We get that
\(p=3+2q\)
Subsituting this value of p into the second and third equation, we get the system with r and q, we get
\(q-2r=-2+q\\ 3+2q+r=9+3+2q\)
Now, focusing on the first equation of the new system, isolating r, we find that
\(r=1\)
Plugging in this value for r into the second equation, we have that
\(3+2q+1=2q+12\\2q+4=2q+12\\-8=0\)
THIS IS DEFINITELY NOT TRUE.
In conclusion, we know that this system has NO SOLUTIONS.
I think this is right...
Thanks! :)
