Question

9))) 5xy = -7y+24 ; X=-1
Gather the Y’s
Answer should be : y=24/5x+7 ; y=12

Answer 1

To solve the equation \(5xy = -7y + 24\) while substituting \(x = -1\) into the equation, we will first replace \(x\) and then gather the \(y\) terms.

1. Substitute \(x = -1\) into the equation:
\[
5(-1)y = -7y + 24
\]
This simplifies to:
\[
-5y = -7y + 24
\]

2. Now, we will gather the \(y\) terms:
\[
-5y + 7y = 24
\]
Simplifying gives us:
\[
2y = 24
\]

3. Now, divide both sides by 2:
\[
y = \frac{24}{2} = 12
\]

So, we have found \(y = 12\).

Now, to rearrange the original equation in terms of \(y\):
From \(5xy = -7y + 24\):
\[
5xy + 7y = 24
\]
Factoring out \(y\) gives:
\[
y(5x + 7) = 24
\]
Now, divide both sides by \(5x + 7\) (assuming \(5x + 7 \neq 0\)):
\[
y = \frac{24}{5x + 7}
\]

Substituting \(x = -1\) into \(y = \frac{24}{5x + 7}\):
\[
y = \frac{24}{5(-1) + 7} = \frac{24}{-5 + 7} = \frac{24}{2} = 12
\]

Thus, the correct representation matches:
- \(y = \frac{24}{5x + 7}\)
- \(y = 12\) when \(x = -1\).

Final answer is:
\[
y = \frac{24}{5x + 7} \quad \text{and} \quad y = 12
\]