For a pair of linear equations, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which statement about their graphical representation is correct?
Answer and explanation
Correct answer: The lines are distinct parallel lines and have no solution.
Equal ratios of \(a\) and \(b\) give the two lines the same slope. Since the \(c\)-ratios differ, the lines cannot coincide; they are distinct parallel lines with no solution. Exam tip: always compare all three ratios.
Frequently asked questions
What is the correct answer to this question?
The lines are distinct parallel lines and have no solution.
Why is this the correct answer?
Equal ratios of \(a\) and \(b\) give the two lines the same slope. Since the \(c\)-ratios differ, the lines cannot coincide; they are distinct parallel lines with no solution. Exam tip: always compare all three 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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