nguyendinhtuong wrote:
(2) \(b=a+1 \implies \frac{a}{b}= \frac{b-1}{b}=1-\frac{1}{b}=\frac{2}{3} \)
\(\implies \frac{1}{b}=\frac{1}{3} \implies b=3 \implies a=4 \implies a+b=7\).
Great solution, but here, to find a, you added 1 to b, instead of subtracting 1 from b (the solution should be a=2 and b=3).
I find the wording of the question very problematic. When I first read the question:
"The equations ax + 2y = 6 and bx + cy = 9 have infinite solutions"
I think 'of course they do, each is one equation with three or four unknowns'. They mean there are infinite solutions when the two equations are solved simultaneously. And they further mean there are infinite solutions specifically for x and y, not for a, b or c. The question needs to say that; someone who has studied a lot of algebra might assume that, because it's a convention that x and y are your 'variables' and early letters in the alphabet are constants, but there's no logical reason that needs to be true.
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