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1957 AMC 12 Question 41

AMC12 · 1957 AMC 12

Question 41

Given the system of equations

$$
\begin{aligned} ax+(a-1)y&=1,\\ (a+1)x-ay&=1. \end{aligned}
$$

For which one of the following values of $a$ is there no solution for $x$ and $y?$
  1. $1$
  2. $0$
  3. $-1$
  4. $\pm\dfrac{\sqrt2}{2}$
  5. $\pm\sqrt2$