For the pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), which statement about their graphs is correct?
Answer and explanation
Correct answer: The lines will be distinct and parallel
When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines have the same slope but are not the same line. Hence, they are distinct parallel lines and have no common point. Coincident lines require all three ratios to be equal, while intersecting lines require the first two ratios to be unequal. Exam tip: Compare the ratios in the order \(a\), \(b\), and \(c\) to identify the graphical condition.
Frequently asked questions
What is the correct answer to this question?
The lines will be distinct and parallel
Why is this the correct answer?
When \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines have the same slope but are not the same line. Hence, they are distinct parallel lines and have no common point. Coincident lines require all three ratios to be equal, while intersecting lines require the first two ratios to be unequal. Exam tip: Compare the ratios in the order \(a\), \(b\), and \(c\) to identify the graphical condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
