What is the correct solution status for the equations (17x+6y=52) and (8x+3y=25)?
Answer and explanation
Correct answer: One unique solution
For a pair of linear equations, if \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), the two lines intersect at exactly one point and have a unique solution. Here, \(\frac{17}{8}\ne\frac{6}{3}\), so the correct status is one unique solution. Infinitely many solutions would require all three corresponding ratios to be equal. Exam tip: first compare the ratios of the coefficients of \(x\) and \(y\).
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For a pair of linear equations, if \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), the two lines intersect at exactly one point and have a unique solution. Here, \(\frac{17}{8}\ne\frac{6}{3}\), so the correct status is one unique solution. Infinitely many solutions would require all three corresponding ratios to be equal. Exam tip: 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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