For infinitely many solutions of (3x+ay=6) and (9x+12y=b), what is ((a,b))?
Answer and explanation
Correct answer: \((4,18)\)
For infinitely many solutions, both equations must represent the same line. Hence, \(\frac{3}{9}=\frac{a}{12}=\frac{6}{b}\). Since \(\frac{3}{9}=\frac{1}{3}\), we get \(a=4\) and \(b=18\). In \((4,12)\), \(\frac{6}{b}=\frac{1}{2}\), so it cannot give infinitely many solutions. Exam tip: for infinitely many solutions, equate all three coefficient ratios.
Frequently asked questions
What is the correct answer to this question?
\((4,18)\)
Why is this the correct answer?
For infinitely many solutions, both equations must represent the same line. Hence, \(\frac{3}{9}=\frac{a}{12}=\frac{6}{b}\). Since \(\frac{3}{9}=\frac{1}{3}\), we get \(a=4\) and \(b=18\). In \((4,12)\), \(\frac{6}{b}=\frac{1}{2}\), so it cannot give infinitely many solutions. Exam tip: for infinitely many solutions, equate all three coefficient ratios.
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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