How many solutions will the equations (6x+11y=29) and (12x+22y=63) have?
Answer and explanation
Correct answer: No solution
For the two equations, 6/12 = 11/22 = 1/2, but 29/63 is not equal to 1/2. Thus, the ratios of the coefficients of x and y are equal, while the ratio of the constant terms is different. This represents two distinct parallel lines, so they have no common point and the pair has no solution. Exam tip: if a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair of linear equations has no solution.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
For the two equations, 6/12 = 11/22 = 1/2, but 29/63 is not equal to 1/2. Thus, the ratios of the coefficients of x and y are equal, while the ratio of the constant terms is different. This represents two distinct parallel lines, so they have no common point and the pair has no solution. Exam tip: if a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair of linear equations has no solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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