What should (k) be for (kx+5y=20) and (6x+10y=45) to have no solution?
Answer and explanation
Correct answer: 3
For two linear equations to have no solution, the ratios of the coefficients of the variables must be equal, but this common ratio must differ from the ratio of the constants. Here, \(k/6=5/10=1/2\), which gives \(k=3\). Also, \(20/45=4/9\), not \(1/2\), so the two lines are distinct and parallel. Therefore, option B is correct. Exam tip: For ‘no solution,’ check \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For two linear equations to have no solution, the ratios of the coefficients of the variables must be equal, but this common ratio must differ from the ratio of the constants. Here, \(k/6=5/10=1/2\), which gives \(k=3\). Also, \(20/45=4/9\), not \(1/2\), so the two lines are distinct and parallel. Therefore, option B is correct. Exam tip: For ‘no solution,’ check \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
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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