Which condition is correct for (11x+py=33) and (4x+2y=15) to have a unique solution?
Answer and explanation
Correct answer: \(p\ne\frac{11}{2}\)
For two linear equations to have a unique solution, the ratios of the coefficients of the two variables must be unequal: \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\). Here, \(\frac{a_1}{a_2}=\frac{11}{4}\) and \(\frac{b_1}{b_2}=\frac{p}{2}\). Thus, \(\frac{11}{4}\ne\frac{p}{2}\), which gives \(p\ne\frac{11}{2}\). Therefore, option B is correct. In option A, the two ratios become equal, so the system cannot have a unique solution. Exam tip: For a unique solution, check that the ratios of the corresponding variable coefficients are unequal.
Frequently asked questions
What is the correct answer to this question?
\(p\ne\frac{11}{2}\)
Why is this the correct answer?
For two linear equations to have a unique solution, the ratios of the coefficients of the two variables must be unequal: \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\). Here, \(\frac{a_1}{a_2}=\frac{11}{4}\) and \(\frac{b_1}{b_2}=\frac{p}{2}\). Thus, \(\frac{11}{4}\ne\frac{p}{2}\), which gives \(p\ne\frac{11}{2}\). Therefore, option B is correct. In option A, the two ratios become equal, so the system cannot have a unique solution. Exam tip: For a unique solution, check that the ratios of the corresponding variable coefficients are unequal.
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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