What is the correct ratio relation for (6x-7y+9=0) and (12x-14y+25=0)?
Answer and explanation
Correct answer: \(\frac{6}{12}=\frac{-7}{-14}\ne\frac{9}{25}\)
For two linear equations, the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\) represents distinct parallel lines, so the pair has no solution. Here, \(\frac{6}{12}=\frac{-7}{-14}=\frac{1}{2}\), whereas \(\frac{9}{25}\ne\frac{1}{2}\). Therefore, option A is correct. Exam tip: compare the ratios of the coefficients of \(x\) and \(y\) first, and then compare them with the constant-term ratio.
Frequently asked questions
What is the correct answer to this question?
\(\frac{6}{12}=\frac{-7}{-14}\ne\frac{9}{25}\)
Why is this the correct answer?
For two linear equations, the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\) represents distinct parallel lines, so the pair has no solution. Here, \(\frac{6}{12}=\frac{-7}{-14}=\frac{1}{2}\), whereas \(\frac{9}{25}\ne\frac{1}{2}\). Therefore, option A is correct. Exam tip: compare the ratios of the coefficients of \(x\) and \(y\) first, and then compare them with the constant-term ratio.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
