QQuestionMathematics
QuestionMathematics
Given the equation 3(x + y) = y, if (x, y) is a solution to the equation and y cannot equal zero, what is the ratio
x/y?
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Answer
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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely:
Step 2:: Expand the left side of the equation
3(x + y) = y
3x + 3y = y
Step 3:: Subtract y from both sides
3x + 3y - y = 0
3x + 2y = 0
Step 4:: Rearrange to isolate x
3x = -2y
Step 5:: Solve for x/y ratio
x = -\frac{2}{3}y
Step 6:: Calculate the ratio x/y
\frac{x}{y} = -\frac{2}{3}
Final Answer
Key Insights: - The solution requires algebraic manipulation - We used the constraint that y ≠ 0 - The ratio is a constant value of -\frac{2}{3}
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