Solution
= Solution
Move the right-hand side to the left. The resulting <homogeneous linear system> has coefficient <matrix>
$$
\begin{pmatrix}-2&1\\1&b-2\end{pmatrix}.
$$
A nonzero solution exists exactly when its <determinant> vanishes:
$$
\boxed{(-2)(b-2)-1=0}.
$$
Here the upper-left entry of the original <matrix> is $-1$, as verified in the original PDF; that entry is corrupted in the local OCR.