Which statement is correct by observing the equations (18x+13y=89) and (36x+26y=178)?
Answer and explanation
Correct answer: Lines are the same
The second equation is exactly twice the first: multiplying \(18x+13y=89\) by 2 gives \(36x+26y=178\). Hence, both equations represent the same line and the pair has infinitely many solutions. Option A is incorrect because distinct parallel lines have equal ratios of the coefficients of \(x\) and \(y\), but a different ratio for the constant terms. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); if all three ratios are equal, the lines are coincident.
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What is the correct answer to this question?
Lines are the same
Why is this the correct answer?
The second equation is exactly twice the first: multiplying \(18x+13y=89\) by 2 gives \(36x+26y=178\). Hence, both equations represent the same line and the pair has infinitely many solutions. Option A is incorrect because distinct parallel lines have equal ratios of the coefficients of \(x\) and \(y\), but a different ratio for the constant terms. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\); if all three ratios are equal, the lines are coincident.
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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