Choose the correct option for (13x+4y=6) and (26x+8y=12).
Answer and explanation
Correct answer: Infinitely many solutions
Here, \(\frac{a_1}{a_2}=\frac{13}{26}=\frac{1}{2}\), \(\frac{b_1}{b_2}=\frac{4}{8}=\frac{1}{2}\), and \(\frac{c_1}{c_2}=\frac{6}{12}=\frac{1}{2}\). Therefore, both equations represent the same line, so the pair has infinitely many solutions. Option B would be correct only if the first two ratios were equal but the third ratio were different. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the pair has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
Infinitely many solutions
Why is this the correct answer?
Here, \(\frac{a_1}{a_2}=\frac{13}{26}=\frac{1}{2}\), \(\frac{b_1}{b_2}=\frac{4}{8}=\frac{1}{2}\), and \(\frac{c_1}{c_2}=\frac{6}{12}=\frac{1}{2}\). Therefore, both equations represent the same line, so the pair has infinitely many solutions. Option B would be correct only if the first two ratios were equal but the third ratio were different. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the pair has infinitely many solutions.
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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