The dots mark where lines ℓ₁ and ℓ₂ cross the axes (1 square = 1 unit). Which pair of equations do the two lines represent?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations

Aℓ₁: $2 x + y = 6$ , ℓ₂: $x - y = 3$
Bℓ₁: $x + 2 y = 6$ , ℓ₂: $x - y = 3$
Cℓ₁: $x + 2 y = 6$ , ℓ₂: $x + y = 3$
Dℓ₁: $x + 2 y = 6$ , ℓ₂: $y - x = 3$

Step-by-Step Solution

ℓ_{1}

passes through

(6, 0)

and

(0, 3) : 6 + 2 (0) = 6, 0 + 2 (3) = 6

, so

x + 2 y = 6. ℓ_{2}

passes through

(3, 0)

and

(0, - 3) : 3 - 0 = 3, 0 - (- 3) = 3

, so

x - y = 3

Answer: B) ℓ₁:

x + 2 y = 6

, ℓ₂:

x - y = 3

Key idea: Word problems and translation

Most Class 10 questions on this topic are word problems. The skill is in TRANSLATION:

1. Identify the two unknowns; assign variables (e.g., let

x

= age of A,

y

= age of B).
2. Write two equations from the two given pieces of information.
3. Solve by your preferred method.

**Common types**:
- **Age problems**: 'Father is twice as old as son. Five years ago father was three times. Find ages.'
- **Number problems**: 'A two-digit number plus its reverse is 99...'
- **Distance/time/speed**: 'Boat in still water speeds, downstream/upstream rates...'
- **Cost problems**: 'Cost of pencils and pens.'
- **Fraction problems**: 'A fraction becomes 1/2 when 1 is added to numerator and 2 is subtracted from denominator...'

Always CHECK by substituting solution back into the original word problem (not just the equations).

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