What is the value of a for the pair of equations 3x + ay = 12 and 6x + 8y = 24 to have infinitely many solutions?
Answer and explanation
Correct answer: 4
For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, infinitely many solutions occur when a₁/a₂ = b₁/b₂ = c₁/c₂. Here the corresponding ratios are 3/6, a/8, and 12/24. Since 3/6 = 12/24 = 1/2, we must have a/8 = 1/2. Multiplying by 8 gives a = 4. Therefore, option B is correct. Option A, C, and D do not make all three ratios equal, so they would not represent coincident lines and cannot produce infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, infinitely many solutions occur when a₁/a₂ = b₁/b₂ = c₁/c₂. Here the corresponding ratios are 3/6, a/8, and 12/24. Since 3/6 = 12/24 = 1/2, we must have a/8 = 1/2. Multiplying by 8 gives a = 4. Therefore, option B is correct. Option A, C, and D do not make all three ratios equal, so they would not represent coincident lines and cannot produce infinitely many common solutions.
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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