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The graph shows the monthly bill of two mobile plans for different numbers of call minutes. Simran talks for about 70 minutes a month (dashed line). Which plan is cheaper for her, and by how much?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • APlan B, by ₹40
  • BPlan A, by ₹20
  • CBoth plans cost the same
  • DPlan A, by ₹40

Step-by-Step Solution

The lines cross at 50 minutes (both ₹200); after that Plan A is lower. At 70 minutes Plan A and Plan B , so Plan A is cheaper by .
Answer: D) Plan A, by ₹40

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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