To solve the system of equations using substitution, we can start with the first equation, \(-2y = c\), and solve for \(y\):
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Solve for \(y\): \[ y = -\frac{c}{2} \]
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Substitute \(y\) in the second equation: Now we substitute \(-\frac{c}{2}\) for \(y\) in the second equation: \[ 7x + 9y = -45 \] becomes \[ 7x + 9\left(-\frac{c}{2}\right) = -45 \]
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Simplify the equation: \[ 7x - \frac{9c}{2} = -45 \]
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Isolate \(x\): Let's first move \(-\frac{9c}{2}\) to the right side: \[ 7x = -45 + \frac{9c}{2} \] Now, divide by 7 to solve for \(x\): \[ x = \frac{-45 + \frac{9c}{2}}{7} \]
So, we have: \[ x = \frac{-45 + \frac{9c}{2}}{7} \] and \[ y = -\frac{c}{2} \]
This gives us the values of \(x\) and \(y\) in terms of \(c\): \[ x = \frac{-90 + 9c}{14} \] \[ y = -\frac{c}{2} \]
These expressions represent the solution to the system in terms of \(c\). If you have a specific value for \(c\), you can substitute it to find the numerical values of \(x\) and \(y\).
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