When will ((p+4)x-9y=2) and (5x-15y=6) have a unique solution?
Answer and explanation
Correct answer: \(p\neq -1\)
A pair of linear equations has a unique solution when the ratios of the coefficients of x and y are unequal. Here, the condition is \(\frac{p+4}{5}\neq\frac{-9}{-15}\). Since \(\frac{-9}{-15}=\frac{3}{5}\), we need \(\frac{p+4}{5}\neq\frac{3}{5}\), which gives \(p\neq -1\). At \(p=-1\), the x- and y-coefficient ratios become equal, so the solution cannot be unique. Exam tip: for a unique solution, first compare the ratios of the coefficients of x and y.
Frequently asked questions
What is the correct answer to this question?
\(p\neq -1\)
Why is this the correct answer?
A pair of linear equations has a unique solution when the ratios of the coefficients of x and y are unequal. Here, the condition is \(\frac{p+4}{5}\neq\frac{-9}{-15}\). Since \(\frac{-9}{-15}=\frac{3}{5}\), we need \(\frac{p+4}{5}\neq\frac{3}{5}\), which gives \(p\neq -1\). At \(p=-1\), the x- and y-coefficient ratios become equal, so the solution cannot be unique. Exam tip: for a unique solution, first compare the ratios of the coefficients of x and y.
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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