To determine how many solutions the equation \( y + 7 = y - 3 \) has, we can start by simplifying the equation.
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Subtract \( y \) from both sides:
\[ 7 = -3 \]
This statement, \( 7 = -3 \), is a contradiction. Therefore, there are no values of \( y \) that can satisfy this equation.
So the correct response is:
no solutions