Based on the description provided, the correct system of equations is:
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x increased by 3 is equal to the product of 2 and y: This can be written as: \[ x + 3 = 2y \]
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5 times y is equal to negative x minus 10: This can be expressed as: \[ 5y = -x - 10 \]
Therefore, the correct system of equations is: \[ \begin{cases} x + 3 = 2y \ 5y = -x - 10 \end{cases} \]
From the given responses, the correct one is: \[ {x + 3 = 2y, \ 5y = -x - 10} \]