- A
- B
- C
- D
Step-by-Step Solution
Cross-multiplication gives , so .
Answer: A)
By the cross-multiplication formula for and , the value of equals:
Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
Key idea: Cross-multiplication method
For a₁ + b₁ + c₁ = 0 and a₂ + b₂ + c₂ = 0, the solution (when unique) is:
/ (b₁c₂ − b₂c₁) = / (c₁a₂ − c₂a₁) = 1 / (a₁b₂ − a₂b₁).
From these:
= (b₁c₂ − b₂c₁) / (a₁b₂ − a₂b₁)
= (c₁a₂ − c₂a₁) / (a₁b₂ − a₂b₁)
**Caveat**: this works ONLY if (a₁b₂ − a₂b₁) ≠ 0 (i.e., lines aren't parallel/coincident).
Useful when you've memorised the formula and want to skip elimination steps.
/ (b₁c₂ − b₂c₁) = / (c₁a₂ − c₂a₁) = 1 / (a₁b₂ − a₂b₁).
From these:
= (b₁c₂ − b₂c₁) / (a₁b₂ − a₂b₁)
= (c₁a₂ − c₂a₁) / (a₁b₂ − a₂b₁)
**Caveat**: this works ONLY if (a₁b₂ − a₂b₁) ≠ 0 (i.e., lines aren't parallel/coincident).
Useful when you've memorised the formula and want to skip elimination steps.
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