- A1
- B3
- C4
- D2
Step-by-Step Solution
Multiply by 10: and . Multiply first by 2: . Subtract: . Then → .
Answer: D) 2
Solve: and . Find .
Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
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.
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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