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Solve by elimination: and . Find .

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A−3
  • B4
  • C−4
  • D3

Step-by-Step Solution

Multiply the first by 4 and the second by 5 so the -terms match: and . Subtract: → , and then → . Check: ✓. Answering −3 reports instead of , and subtracting the wrong way round flips the sign to −4.
Answer: B) 4

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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