Certainly! Let's start with the given equation:
\[ 5xy = -7y + 24 \]
We want to isolate \(y\) on one side of the equation. First, we can rearrange the equation to put all terms involving \(y\) on one side. Let's rewrite the equation:
\[ 5xy + 7y = 24 \]
Next, we can factor out \(y\) from the left side:
\[ y(5x + 7) = 24 \]
Now, to solve for \(y\), we can divide both sides by \((5x + 7)\):
\[ y = \frac{24}{5x + 7} \]
Now we substitute \(x = -1\) into the equation to find the value of \(y\):
\[ y = \frac{24}{5(-1) + 7} \]
Now let's simplify the denominator:
\[ y = \frac{24}{-5 + 7} \] \[ y = \frac{24}{2} \] \[ y = 12 \]
So, when \(x = -1\), the value of \(y\) is \(12\).
Therefore, the solution to the problem is:
- \(y = \frac{24}{5x + 7}\)
- \(y = 12\) when \(x = -1\).