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1975 AMC 12 Question 2

AMC12 · 1975 AMC 12

Question 2

For which real values of $m$ are the simultaneous equations $$
\begin{aligned} y&=mx+3,\\ y&=(2m-1)x+4 \end{aligned}
$$ satisfied by at least one pair of real numbers $(x,y)?$
  1. all $m$
  2. all $m\ne0$
  3. all $m\ne\frac12$
  4. all $m\ne1$
  5. no values of $m$