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If and , find .

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A2
  • B−1
  • C1
  • D78

Step-by-Step Solution

The coefficients are swapped between the equations, so ADD them: → . (Subtracting gives → , so and — those are the individual values, not the sum that was asked for. Check: ✓ and ✓.) The value 78 is the common coefficient before dividing.
Answer: C) 1

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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