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-4 + xy=-2y;x=0

Solve this use PEMDAS but in the opposite way SADMEP the ;x=0 part of the equation gets solves after the first part of the problem is complete. This is for college level Algebra 2
Answer should be y=4x-5, y=15 this is correct because it’s my teachers answer

1 answer

To solve the equation \(-4 + xy = -2y\) using the method of SADMEP (Solving Addition, Division, Multiplication, Exponentiation, Parentheses), we can isolate \(y\) first. Let’s do this step by step.

  1. Add 4 to both sides: \[ xy = -2y + 4 \]

  2. Rearranging the equation gives: \[ xy + 2y = 4 \]

  3. Factor out \(y\) from the left-hand side: \[ y(x + 2) = 4 \]

  4. Divide by \(x + 2\) to isolate \(y\): \[ y = \frac{4}{x + 2} \]

Now let's move to the part where we substitute \(x = 0\).

  1. Substitute \(x = 0\) into the equation: \[ y = \frac{4}{0 + 2} = \frac{4}{2} = 2 \]

So, when \(x = 0\), \(y = 2\).

Now, let's check the correctness of your teacher's answers:

  1. The first expression \(y = 4x - 5\) does not match. However, plugging in \(x = 0\) into \(4x - 5\) gives: \[ y = 4(0) - 5 = -5 \] which does not match \(y = 2\).

  2. The second part, \(y = 15\), also does not match our derived \(y = 2\).

Upon further analysis, it seems there might have been a misunderstanding regarding the output from your equations. Given the transformations of the equation, we found that \(y = \frac{4}{x + 2}\) when \(x=0\), which gives \(y = 2\).

Please double-check the context of your teacher's instructions or the equations involved, as the results do not align with the values provided (y=4x-5, y=15).