Equations and Inequations - Formula Sheet
🔢 Equations and Inequations - Formula Sheet
🎯 Linear Equations
Single Variable
ax + b = 0 Solution: x = -b/a
Two Variables
a₁x + b₁y = c₁ a₂x + b₂y = c₂
Methods:
- Substitution: Express one variable in terms of other
- Elimination: Make coefficients equal and eliminate
- Cross-multiplication: (x/c₁) = (y/c₂) when a₁b₂ = a₂b₁
📊 Quadratic Equations
Standard Form
ax² + bx + c = 0
Solutions
x = [-b ± √(b² - 4ac)] / 2a
Discriminant
Δ = b² - 4ac Δ > 0: Two real roots Δ = 0: One real root Δ < 0: No real roots
🔢 Inequalities
Linear Inequalities
ax + b > 0 → x > -b/a (if a > 0) ax + b > 0 → x < -b/a (if a < 0)
Quadratic Inequalities
ax² + bx + c > 0
- Find roots
- Draw sign diagram
- Identify solution intervals
⚡ Special Cases
Ratio Problems
If a:b = c:d, then ad = bc
Age Problems
Current age = x Age after n years = x + n Age n years ago = x - n
Number Problems
Two-digit number: 10x + y Three-digit number: 100x + 10y + z
📝 Solving Steps
- Identify variables
- Form equations from statements
- Choose appropriate method
- Solve systematically
- Verify solution
Master Equations - Practice makes perfect! 🔢
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