Final answer:
To solve the equation \(\frac{-4x-2y}{x-2y} = \frac{-2}{9}\), cross multiply and combine like terms to solve for \(y\), resulting in the solution \(y = \frac{-17x}{11}\).
Step-by-step explanation:
The given equation is:
\(\frac{-4x-2y}{x-2y} = \frac{-2}{9}\)
To solve for \(x\) and \(y\), we can cross multiply:
\((-4x-2y) \cdot 9 = (-2) \cdot (x-2y)\)
Simplifying both sides of the equation:
\(-36x - 18y = -2x + 4y\)
Combining like terms:
\(-36x + 2x = 4y + 18y\)
\(-34x = 22y\)
Dividing both sides by \(22\) to solve for \(y\):
\(y = \frac{-34x}{22}\)
Therefore, the solution for the equation is \(y = \frac{-17x}{11}\).