Solution
= Solution
{c}
The first two equations give $x_1=1-2x_3$ and $x_2=2-5x_3$. Substitution into the third gives
$$
(\lambda-5)x_3=\mu-2.
$$
This equation is inconsistent exactly when its left side is identically zero and its right side is nonzero. Therefore
$$
\boxed{\text{no solution}\iff\lambda=5,\quad\mu\ne2.}
$$