If $x^2 + xy = 12$ and $2xy + 3y^2 + 5 = 0$ then $x + 4y$ is equal to:
Step-by-Step Solution
Key Concept: Adding two equations strategically can create a factorable expression that yields multiple solutions.
Given $5x^2 + 5xy = 60$ and $24y + 36y^2 = -60$, we add both equations to get $5x^2 + 5xy + 24y + 36y^2 = 0$. Factoring this expression yields $(x + 4y)(5x + 9y) = 0$, giving the solutions.
Correct Answer: 1