xy=4 and xy> 0

Step 1 ：The given equations are \(xy = 4\) and \(xy > 0\).

Step 2 ：Since \(xy > 0\), both x and y are positive numbers.

Step 3 ：We can solve for x by dividing both sides of the equation \(xy = 4\) by y, which gives us \(x = \frac{4}{y}\).

Step 4 ：Let's assume y = 1, then substituting y into the equation gives us \(x = \frac{4}{1} = 4.0\).

Step 5 ：Now that we have solved for x, we can substitute x into the equation to solve for y.

Step 6 ：Substituting x = 4.0 into the equation \(xy = 4\) gives us \(4y = 4\), which simplifies to \(y = 1.0\).

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = 4.0, y = 1.0}\).