Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p
+8 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.
