What value of (k) makes (3x+ky=9) and (6x+8y=20) have no solution?
Answer and explanation
Correct answer: 4
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). Here, \(\frac{3}{6}=\frac{k}{8}\), which gives \(k=4\). Also, \(\frac{9}{20}\neq\frac{1}{2}\), so the two lines are parallel and inconsistent. Exam tip: first equate the ratios of the variable coefficients, then check that the ratio of the constants is different.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). Here, \(\frac{3}{6}=\frac{k}{8}\), which gives \(k=4\). Also, \(\frac{9}{20}\neq\frac{1}{2}\), so the two lines are parallel and inconsistent. Exam tip: first equate the ratios of the variable coefficients, then check that the ratio of the constants is different.
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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