For a pair of linear equations in two variables, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), what is the position of their lines?
Answer and explanation
Correct answer: They are distinct parallel lines
When \(a_1/a_2=b_1/b_2\), the two lines have the same slope. Since \(c_1/c_2\) is different, they cannot be the same line; hence they are distinct parallel lines with no solution. Exam tip: equal first two ratios and an unequal third ratio indicate an inconsistent pair.
Frequently asked questions
What is the correct answer to this question?
They are distinct parallel lines
Why is this the correct answer?
When \(a_1/a_2=b_1/b_2\), the two lines have the same slope. Since \(c_1/c_2\) is different, they cannot be the same line; hence they are distinct parallel lines with no solution. Exam tip: equal first two ratios and an unequal third ratio indicate an inconsistent pair.
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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