What is the value of q for infinitely many solutions of qx + 11y = 22 and 18x + 33y = 66?
Answer and explanation
Correct answer: q = 6
For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have infinitely many solutions, the coefficients must satisfy a₁/a₂ = b₁/b₂ = c₁/c₂. Comparing qx + 11y = 22 with 18x + 33y = 66 gives q/18 = 11/33 = 22/66. Both known ratios equal 1/3, so q/18 = 1/3 and q = 18/3 = 6. Therefore option C is correct. Values 4, 5, and 7 do not make the coefficient ratios equal, so they would not produce coincident lines or infinitely many common points.
Frequently asked questions
What is the correct answer to this question?
q = 6
Why is this the correct answer?
For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have infinitely many solutions, the coefficients must satisfy a₁/a₂ = b₁/b₂ = c₁/c₂. Comparing qx + 11y = 22 with 18x + 33y = 66 gives q/18 = 11/33 = 22/66. Both known ratios equal 1/3, so q/18 = 1/3 and q = 18/3 = 6. Therefore option C is correct. Values 4, 5, and 7 do not make the coefficient ratios equal, so they would not produce coincident lines or infinitely many common points.
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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