Learn the Class 9 Madhyamik Mathematics Linear Simultaneous Equations Formulas with important conditions for unique, infinite, and no solutions, along with the cross multiplication method. Includes formulas, ratio comparisons, graph interpretations, and solved examples for quick understanding and exam preparation.
Chapter 05 – Linear Simultaneous Equation | Class 9 Flash Formula
Important Condition in Simultaneous Equation
| Simultaneous Equation | Comparison of Ratio | On Graph Paper | Conclusion |
|---|---|---|---|
| a₁x + b₁y = c₁ a₂x + b₂y = c₂ |
a₁/a₂ ≠ b₁/b₂ | Two intersecting straight lines | Unique solution |
| a₁x + b₁y = c₁ a₂x + b₂y = c₂ |
a₁/a₂ = b₁/b₂ = c₁/c₂ | Two coincident straight lines | Infinite solution |
| a₁x + b₁y = c₁ a₂x + b₂y = c₂ |
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ | Two non-coincident parallel straight lines | No solution |
Solving Simultaneous Equation by the Method of Cross Multiplication
a₁x + b₁y + c₁ = 0 .......... (i)
a₂x + b₂y + c₂ = 0 .......... (ii)
\text{x} \over (\text{b₁c₂ − b₂c₁}) = \text{y} \over (\text{c₁a₂ − c₂a₁}) = 1 \over (\text{a₁b₂ − a₂b₁})
or
x = \text{(b₁c₂ − b₂c₁)} \over \text{(a₁b₂ − a₂b₁)}
y = \text{(c₁a₂ − c₂a₁)} \over \text{(a₁b₂ − a₂b₁)}
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