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For which value of p does the following system of equations have a solution? p^3x + (p+1)^3y = (p+2)^3 px + (p+1)y = p+2 x + y = 1

1. p = 0
2. p = 1
3. p = -1
4. 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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