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To use cross-multiplication on and , the equations must first be written in the form a₁ + b₁ + c₁ = 0. What are c₁ and c₂?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • Ac₁ = 7, c₂ = 9
  • Bc₁ = −7, c₂ = −9
  • Cc₁ = 7, c₂ = −9
  • Dc₁ = 3, c₂ = −1

Step-by-Step Solution

Move the constants to the left: and , so c₁ = −7 and c₂ = −9. Leaving the constants positive is the standard slip — it flips the sign of every term in the cross-multiplication formula. (c₁ = 3, c₂ = −1 confuses the constants with b₁ and b₂.)
Answer: B) c₁ = −7, c₂ = −9

Key idea: Elimination method

**Steps**:
1. Multiply one or both equations by chosen numbers so coefficients of ONE variable become equal (in magnitude).
2. Add or subtract to ELIMINATE that variable.
3. Solve the resulting one-variable equation.
4. Plug back to find the other.

**Example**: ; .
- Multiply first by 3, second by 4: .
- Add: → . Substituting back gives .

Elimination is faster than substitution when both equations have non-trivial coefficients.

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