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# Algebra

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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

Jul 24, 2024

#1
+1655
+1

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! :)

Jul 24, 2024
edited by NotThatSmart  Jul 24, 2024

#1
+1655
+1

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! :)

NotThatSmart Jul 24, 2024
edited by NotThatSmart  Jul 24, 2024