📐 Simultaneous Equation Solver
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📌 Understanding Simultaneous Equations
A system of two linear equations in two variables is solved using substitution or elimination. The standard form is:
- ax + by = c
- dx + ey = f
- The solution (x, y) is found using the formulas:
- x = (ce – bf) / (ae – bd)
- y = (af – cd) / (ae – bd)
📌 Example Calculations
| a | b | c | d | e | f | Solution (x, y) |
|---|---|---|---|---|---|---|
| 2 | 3 | 6 | 1 | -2 | 3 | (3, 0) |
| 1 | 1 | 5 | 2 | 3 | 10 | (1, 4) |
🔧 Practical Applications of Simultaneous Equations
1. Finance & Economics: Used in market equilibrium and budgeting.
2. Engineering & Physics: Helps in force balancing and circuit analysis.
3. Computer Science: Essential for solving algorithmic problems.
❓ FAQs
Q1: How do I solve a system of equations?
✅ Use the formulas for x and y or apply substitution or elimination.
Q2: What happens if the equations have no solution?
✅ If the determinant (ae – bd) = 0, the system has no unique solution.
Q3: Can simultaneous equations have infinite solutions?
✅ Yes, if the two equations represent the same line.
Q4: Where are simultaneous equations commonly used?
✅ They are widely used in **finance, physics, and engineering**.
Q5: Why are simultaneous equations important?
✅ They help in **solving real-world problems with multiple variables**.