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For which value of p does the following system of equations have a solution?
p³x + (p+1)³y = (p+2)³
px + (p+1)y = p+2
x + y = 1
- p = 0
- p = 1
- p = -1
- p > 1 for every such p
Correct answer: p = -1
Solution
When p = -1, the equations simplify in a way that allows for consistent solutions across all three equations, ensuring that the system is solvable. This value maintains the integrity of the relationships between x and y, making it the only viable option.
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