Understanding the Equations
The problem involves two equations that need to be analyzed and solved step by step.
Equation 1: Simplifying the First Equation
- Start with: 15/x - 2y - 11/3x + 4y = 2
- Combine like terms:
- (15/x - 11/3x) + (-2y + 4y) = 2
- Find a common denominator for the fractions and simplify.
Equation 2: Simplifying the Second Equation
- Start with: 5/2(x + 2y) + 22/3x + 4y = 5/2
- Distribute:
- 5/2 * x + 5/2 * 2y + 22/3x + 4y = 5/2
- Combine like terms:
- Group the x terms and the y terms together.
Finding Common Solutions
- Set both equations equal to each other to find values for x and y.
- Use substitution or elimination methods to solve for one variable in terms of the other.
Final Steps
- Substitute back to find the values of both variables.
- Ensure both equations hold true with the found values.
Conclusion
- Verify your solutions by plugging them back into the original equations.
- Check for any constraints or special conditions that may affect the solutions.
By following these steps, you can systematically solve the given equations and better understand the relationships between the variables involved.