Which statement is correct for the equations (9x+2y=25) and (18x+5y=54)?

Correct answer: \(\frac{9}{18}\ne\frac{2}{5}\), so there is one unique solution

Here, \(\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{2}{5}\). Since \(\frac{1}{2}\ne\frac{2}{5}\), we have \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), so the two lines intersect at exactly one point. Therefore, the pair has a unique solution. Options A and C incorrectly assert equality of ratios, while coincident lines require all three ratios to be equal. In an exam, first compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\) to identify a unique solution quickly.