- A6
- B8
- C4
- D12
Step-by-Step Solution
Clear the fractions first. Multiply the first by 12: . Multiply the second by 4: , so . Then → → and . Check: 6/3 + 8/4 = 4 ✓ and 6/2 − 8/4 = 1 ✓. Answering 8 gives instead of .
Answer: A) 6
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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