To solve the equation 4xy + 2x²y = 0, we start by factoring the expression.
First, we can factor out the common term, which in this case is 2xy:
4xy + 2x²y = 2xy(2 + x) = 0
Now, for the product to be zero, at least one of the factors must be equal to zero. We set each factor to zero:
- 2xy = 0: This can happen if either x = 0 or y = 0. So one part of our solution set is all pairs (x, 0) and (0, y).
- 2 + x = 0: Solving for x, we get x = -2. This means if x = -2, y can be any real number. Thus, we have another part of our solution set as (-2, y).
In conclusion, the complete solution set can be expressed as:
- All points where x = 0 (i.e., the entire y-axis)
- All points where y = 0 (i.e., the entire x-axis)
- The line where x = -2 and y is any real number.