The solution of the equations 2x-3y&=7, 4x-6y&=20 is:

(D) There are an unlimited number of solutions

1954 AMC 12 Problem 12

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12.

The solution of the equations

\begin{aligned} 2x-3y&=7,\\ 4x-6y&=20 \end{aligned}

is:

x=18,

and

y=12

x=0,

and

y=0

There is no solution

There are an unlimited number of solutions

x=8,

and

y=5

Compare the second left-hand side with twice the first

Doubling the first equation would require the right-hand side to be

14

, not

20

The left side of the second equation is exactly twice the left side of the first, but its right side is not twice

7.

The equations would require the same expression to equal both

14

and

20,

which is impossible.

Thus, there is no solution, and the correct answer is C.