Problem

The system is \(3x~+~y~=~10\) and \(x~+~y~=~6\). Transformation A subtracts the complete second equation from the first to get \(2x~=~4\) and keeps \(x~+~y~=~6\). Transformation B subtracts only the \(y\)-terms. Which complete response correctly evaluates the transformations?

Answer choices

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Choice B preserves the solution set because canceling the y-terms is all that matters in elimination, while choice A changes the original system too much.

Neither choice preserves the solution set because any subtraction changes the equations, so you must keep the original system exactly as written.

Both choices preserve the solution set because each one removes y and leads to a simpler equation that should have the same solution.

Choice A preserves the solution set because it subtracts the entire second equation from the first, while choice B subtracts only selected terms and is not a valid elimination step.

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The system is \(3x~+~y~=~10\) and \(x~+~y~=~6\). Transformation A subtracts the complete second equation from the first to get \(2x~=~4\) and keeps \(x~+~y~=~6\). Transformation B subtracts only the \(y\)-terms. Which complete response correctly evaluates the transformations?

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