What is p for no solution in px - 5y = 7 and 12x - 15y = 19?
Answer and explanation
Correct answer: p = 4
For no solution, the two lines must be parallel and distinct. Algebraically, this requires a1/a2 = b1/b2 but c1/c2 must be different. From the y-coefficients, (-5)/(-15) = 1/3. Therefore, p/12 must equal 1/3, which gives p = 4. The constant ratio is 7/19, and this is not equal to 1/3, so the lines are distinct rather than coincident. Consequently, they do not intersect and the pair has no solution. Hence option A is correct; the other values do not make the x-coefficient ratio equal to the y-coefficient ratio.
Frequently asked questions
What is the correct answer to this question?
p = 4
Why is this the correct answer?
For no solution, the two lines must be parallel and distinct. Algebraically, this requires a1/a2 = b1/b2 but c1/c2 must be different. From the y-coefficients, (-5)/(-15) = 1/3. Therefore, p/12 must equal 1/3, which gives p = 4. The constant ratio is 7/19, and this is not equal to 1/3, so the lines are distinct rather than coincident. Consequently, they do not intersect and the pair has no solution. Hence option A is correct; the other values do not make the x-coefficient ratio equal to the y-coefficient ratio.
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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