Let's check the given equation \(16 = -5x - 9y\) and the value \(x = -2\).
- Substitute \(x = -2\) into the equation:
\[ 16 = -5(-2) - 9y \] \[ 16 = 10 - 9y \]
- Rearranging the equation:
\[ 16 - 10 = -9y \] \[ 6 = -9y \] \[ y = -\frac{6}{9} \] \[ y = -\frac{2}{3} \]
So, when \(x = -2\), we find that \(y = -\frac{2}{3}\).
Regarding the equation \(y = \frac{5}{4}x - \frac{16}{6}\):
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The term \(-\frac{16}{6}\) simplifies to \(-\frac{8}{3}\).
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To check if this equation matches the values we found, substitute \(x = -2\) into this new equation:
\[ y = \frac{5}{4}(-2) - \frac{8}{3} \]
- Calculate:
\[ y = -\frac{10}{4} - \frac{8}{3} \] \[ y = -\frac{5}{2} - \frac{8}{3} \]
To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6:
\[ -\frac{5}{2} = -\frac{15}{6} \] \[ -\frac{8}{3} = -\frac{16}{6} \]
Now combine:
\[ y = -\frac{15}{6} - \frac{16}{6} = -\frac{31}{6} \]
This output does not equal \(-\frac{2}{3}\).
Therefore, the equation \(y = \frac{5}{4}x - \frac{16}{6}\) does not provide the correct solution for \(y\) when \(x = -2\). The correct answer is \(y = -\frac{2}{3}\).
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