1954 AMC 12 第 12 题

Question

方程组

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

的解为：

The solution of the equations

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

is:

x=18

，且

y=12

x=18,

and

y=12

x=0

，且

y=0

x=0,

and

y=0

无解

There is no solution

有无穷多个解

There are an unlimited number of solutions

x=8

，且

y=5

x=8,

and

y=5

比较第二个等式的左边与第一个等式左边的两倍

Compare the second left-hand side with twice the first

第一个方程乘以二后，右边应为

14

，而不是

20

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

14

, not

20

第二个方程的左边恰好是第一个方程左边的两倍，但右边不是

7

的两倍。这个方程组要求同一个表达式同时等于

14

和

20

，这是不可能的。

因此方程组无解，正确答案是 C。

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.

其他年份的第 12 题