For no solution in (1/2)x + qy = 3 and 2x + 8y = 5, what is q?
Answer and explanation
Correct answer: q = 2
A pair of linear equations has no solution when the ratios of the coefficients of x and y are equal, but this common ratio is different from the ratio of the constant terms. Here, the x-coefficient ratio is (1/2)/2 = 1/4. To make the lines parallel, the y-coefficient ratio must also be q/8 = 1/4, which gives q = 2. The constant ratio is 3/5, not 1/4, so the equations are inconsistent and have no solution. Therefore option B is correct. Values q = 1, 4, or 8 do not make the two coefficient ratios equal, giving a unique intersection instead.
Frequently asked questions
What is the correct answer to this question?
q = 2
Why is this the correct answer?
A pair of linear equations has no solution when the ratios of the coefficients of x and y are equal, but this common ratio is different from the ratio of the constant terms. Here, the x-coefficient ratio is (1/2)/2 = 1/4. To make the lines parallel, the y-coefficient ratio must also be q/8 = 1/4, which gives q = 2. The constant ratio is 3/5, not 1/4, so the equations are inconsistent and have no solution. Therefore option B is correct. Values q = 1, 4, or 8 do not make the two coefficient ratios equal, giving a unique intersection instead.
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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