What is the relation among all three ratios in (3x+4y=22) and (6x+8y=44)?
Answer and explanation
Correct answer: All three ratios are equal
Here, \(\frac{3}{6}=\frac{4}{8}=\frac{22}{44}=\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), so the two linear equations represent coincident lines and have infinitely many solutions. Exam tip: when all three ratios are equal, the lines are coincident; when only the coefficient ratios are equal, they are parallel; and when the first two ratios are equal but the third differs, the system is inconsistent.
Frequently asked questions
What is the correct answer to this question?
All three ratios are equal
Why is this the correct answer?
Here, \(\frac{3}{6}=\frac{4}{8}=\frac{22}{44}=\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), so the two linear equations represent coincident lines and have infinitely many solutions. Exam tip: when all three ratios are equal, the lines are coincident; when only the coefficient ratios are equal, they are parallel; and when the first two ratios are equal but the third differs, the system is inconsistent.
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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