If x≠0 or 4 and y≠0 or 6, then 2x+3y=12 is equivalent to

1974 AMC 12 Problem 1

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x\ne0

4

and

y\ne0

6,

then

\frac2x+\frac3y=\frac12

is equivalent to

4x+3y=xy

y=\frac{4x}{6-y}

\frac{x}{2}+\frac{y}{3}=2

\frac{4y}{y-6}=x

none of these

Clear all three denominators at once

After multiplying by

2xy,

isolate the terms containing

x

and factor

Multiplying by

2xy

gives

4y+6x=xy,

4y=x(y-6).

Since

y\ne6,

x=\frac{4y}{y-6}.

Therefore, the correct answer is D.