Which statement is correct by observing (8x+3y=17) and (16x+6y=34)?
Answer and explanation
Correct answer: Lines are the same
Dividing every term of the second equation by 2 gives \(8x+3y=17\), which is exactly the first equation. Hence, both equations represent the same line and have infinitely many solutions. Option C is incorrect because distinct parallel lines do not have all three corresponding ratios equal. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the two lines are coincident and the system has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
Lines are the same
Why is this the correct answer?
Dividing every term of the second equation by 2 gives \(8x+3y=17\), which is exactly the first equation. Hence, both equations represent the same line and have infinitely many solutions. Option C is incorrect because distinct parallel lines do not have all three corresponding ratios equal. Exam tip: if \(a_1/a_2=b_1/b_2=c_1/c_2\), the two lines are coincident and the system has infinitely many solutions.
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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