For 4x + 6y = 10 and 2x + 3y = k to have no solution, what should k not be?
Answer and explanation
Correct answer: 5
Write the equations in standard form and compare coefficient ratios. Here a₁/a₂ = 4/2 = 2 and b₁/b₂ = 6/3 = 2. For two linear equations to have no solution, the ratios of the x- and y-coefficients must be equal, but the ratio of constant terms must be different: a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Thus we need 10/k ≠ 2. Equality would occur when 10/k = 2, which gives k = 5. At k = 5, the second equation multiplied by 2 becomes the first, so the lines coincide and there are infinitely many solutions. Therefore k must not be 5, making option A correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Write the equations in standard form and compare coefficient ratios. Here a₁/a₂ = 4/2 = 2 and b₁/b₂ = 6/3 = 2. For two linear equations to have no solution, the ratios of the x- and y-coefficients must be equal, but the ratio of constant terms must be different: a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Thus we need 10/k ≠ 2. Equality would occur when 10/k = 2, which gives k = 5. At k = 5, the second equation multiplied by 2 becomes the first, so the lines coincide and there are infinitely many solutions. Therefore k must not be 5, making option A correct.
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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