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2y=-3xy-5; x=1

Answer to this problem above is y= -5/3x+2 : y=-1
Don’t plug in the x value intel the first half of the problem is solved so that its answer is y= -5/3x+2 please thank you

1 answer

To solve for \( y \) in the equation \( 2y = -3xy - 5 \), we can start by isolating \( y \).

  1. Start with the equation:

    \[ 2y = -3xy - 5 \]

  2. Rearrange the equation to group the \( y \) terms:

    \[ 2y + 3xy = -5 \]

  3. Factor out \( y \) on the left side:

    \[ y(2 + 3x) = -5 \]

  4. Now, solve for \( y \) by dividing both sides by \( (2 + 3x) \):

    \[ y = \frac{-5}{2 + 3x} \]

This is the expression for \( y \) in terms of \( x \).

Now, substituting \( x = 1 \) to find the specific value of \( y \):

\[ y = \frac{-5}{2 + 3(1)} = \frac{-5}{2 + 3} = \frac{-5}{5} = -1 \]

So the answer is \( y = -1 \) when \( x = 1 \).

If you meant to express the equation in slope-intercept form (like \( y = mx + b \)), notice that \( \frac{-5}{2 + 3x} \) can't be rewritten into the form you mentioned, as it represents a rational function.

However, if you want to represent this in a linear form involving \( x \) and \( y \), you'd need to appropriately analyze the structure given the \( x \) value.

The conclusion is:

  1. The derived formula for \( y \) is \( y = \frac{-5}{2 + 3x} \).
  2. For \( x = 1 \), \( y = -1 \).

If you're looking for another interpretation or simplification, please clarify!