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Which substitution turns the pair and into a pair of LINEAR equations?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A and
  • B and
  • C and
  • D and

Step-by-Step Solution

The variables appear only as and , so naming those and gives and — a genuine linear pair. Renaming and themselves changes nothing, squaring makes it worse, and replacing and does not clear the denominators.
Answer: A) and

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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