Which conclusion is correct by observing (6x+12y=18) and (x+2y=4)?
Answer and explanation
Correct answer: First two ratios are equal but the constant ratio is different
Compare the coefficients in standard form: \(a_1/a_2=6/1=6\), \(b_1/b_2=12/2=6\), but \(c_1/c_2=18/4=9/2\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel, and the pair has no solution. Option A is incorrect because all three ratios are not equal. Exam tip: remember the no-solution condition as \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
First two ratios are equal but the constant ratio is different
Why is this the correct answer?
Compare the coefficients in standard form: \(a_1/a_2=6/1=6\), \(b_1/b_2=12/2=6\), but \(c_1/c_2=18/4=9/2\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel, and the pair has no solution. Option A is incorrect because all three ratios are not equal. Exam tip: remember the no-solution condition as \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
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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