- A
- B
- C
- D
Step-by-Step Solution
The solution is the point where the two lines meet. They cross at , so . Points where a line meets an axis are not solutions of the pair.
Answer: A)
Lines ℓ₁ and ℓ₂ are the graphs of a pair of linear equations in and (1 square = 1 unit). Read the solution of the pair from the graph.
Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
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 = age of A, = 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).
1. Identify the two unknowns; assign variables (e.g., let = age of A, = 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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Practice 5 Similar Questions Free →All Pair of Linear Equations in Two Variables practice questions
More Class 10 Pair of Linear Equations in Two Variables practice
Meera plotted both equations of a pair on the same grid and got lines ℓ₁ and ℓ₂ shown.…Kabir drew 2x − y = 2 (thick blue line) and 4x − 2y = 4 (dashed orange line) on the same…The lines x − y + 1 = 0 and 3x + 2y − 12 = 0 are drawn on the grid (1 square = 1 unit).…Lines ℓ₁ and ℓ₂ and the x-axis enclose the shaded triangle. Using the grid (1 square = 1…The dots mark where lines ℓ₁ and ℓ₂ cross the axes (1 square = 1 unit). Which pair of…