Understanding the Equation
The given equations appear to involve variables x and y, along with percentages. To analyze them, we first need to clarify the structure and isolate the variables.
Equations Breakdown
1. First Equation:
- 15%x + 2y - 11%3x + 4y = 2
- Simplifying this equation involves converting percentages to decimals and reorganizing terms.
2. Second Equation:
- 5%2(x - 2y) + 22%3x + 4y = 5%2
- Similar simplification is needed here. Again, converting percentages to their decimal equivalents will help.
Conversion of Percentages
- 15% = 0.15
- 11% = 0.11
- 5% = 0.05
- 22% = 0.22
This will allow for clearer calculations when solving for x and y.
Solving the Equations
- Step 1: Convert the percentages.
- Step 2: Rearrange the equations to isolate terms involving x and y.
- Step 3: Use substitution or elimination methods to solve the system of equations.
Final Thoughts
To effectively solve these equations, it is essential to be methodical in your approach, ensuring that each step is followed carefully. The results will yield the values for x and y that satisfy both equations, which is crucial for UPSC problem-solving.
Engaging with these types of equations enhances mathematical reasoning and is a valuable skill in competitive exams. Always practice similar problems to strengthen your understanding.