To solve the system of equations 2xy = 7 and 5xy = 9, we can start by isolating one variable in terms of the other from one of the equations. In this case, both equations involve the product of x and y, so let’s first express y in terms of x from the first equation.
1. **Start with the first equation:**
2xy = 7
We can isolate y:
y = 7 / (2x)
2. **Substitute y in the second equation:**
Now, plug y = 7 / (2x) into the second equation 5xy = 9:
5x(7 / (2x)) = 9
3. **Simplify the equation:**
35 / 2 = 9
4. **Solve for x:**
To solve for x, multiply both sides by 2:
35 = 18
This is a contradiction, indicating that there is no solution for x and y that satisfies both equations simultaneously.
5. **Conclusion:**
Since the two equations lead to a contradiction, we can conclude that the system of equations 2xy = 7 and 5xy = 9 has no solution. In other words, the lines represented by these equations do not intersect on the coordinate plane.