To solve the equation \(-\frac{5}{8}y = \frac{25}{16}\), follow these steps:
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Isolate \(y\): First, we can get \(y\) by multiplying both sides of the equation by the reciprocal of \(-\frac{5}{8}\).
The reciprocal of \(-\frac{5}{8}\) is \(-\frac{8}{5}\).
\[ y = \frac{25}{16} \cdot -\frac{8}{5} \]
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Multiply the fractions:
\[ y = \frac{25 \cdot -8}{16 \cdot 5} \]
Calculating the numerator and the denominator:
\[ y = \frac{-200}{80} \]
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Simplify the fraction:
Dividing both the numerator and the denominator by 40:
\[ y = \frac{-5}{2} \]
Thus, the solution to the equation \(-\frac{5}{8}y = \frac{25}{16}\) is:
\[ y = -\frac{5}{2} \]