Bunuel wrote:
The equations ax + 2y = 6 and bx + cy = 9 have infinite solutions. What is the value of (a + b)?
(1) c = 3
(2) b = a + 1
As given condition, we conclude that those two equations are identical.
Hence \(\frac{a}{b}=\frac{2}{c}=\frac{6}{9}=\frac{2}{3}\)
\(\frac{2}{c} = \frac{2}{3} \implies c=3\)
(1) \(c=3\). No information about \(a\) and \(b\). Insufficient.
(2) \(b=a+1 \implies \frac{a}{b}= \frac{b-1}{b}=1-\frac{1}{b}=\frac{2}{3} \)
\(\implies \frac{1}{b}=\frac{1}{3} \implies b=3 \implies
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