- A4 km, fare ₹90
- B10 km, fare ₹200
- C5 km, fare ₹100
- D6 km, fare ₹110
Step-by-Step Solution
The two lines meet at . City Cab: ; Metro Taxi: km and fare .
Answer: C) 5 km, fare ₹100
The graph shows the fare of two taxi services in Pune for different distances. For what distance are the two fares equal, and what is that fare?
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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