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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

 Jun 20, 2023
 #1
avatar+8 
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Let's solve the system of equations step by step to find the ordered triple (p, q, r) that satisfies the given equations:

Equation 1: p - 2q = 3

Equation 2: q - 2r = -2 + q
Simplifying: -2r = -2

Equation 3: p + r = 9 + p
Simplifying: r = 9

From Equation 2, we found that -2r = -2. Dividing both sides by -2 gives us r = 1.

Now, we can substitute the values of r into the other equations to find the remaining variables:

From Equation 3: p + 1 = 9 + p
Simplifying, we see that 1 = 9, which is not true. Therefore, there is no solution for p in this system of equations.

Since there is no solution for p, q and r cannot be determined. The system of equations is inconsistent and does not have an ordered triple (p, q, r) that satisfies all the equations simultaneously.

 Jun 20, 2023
 #2
avatar+123 
0

Good answer.

 Jun 20, 2023

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