[latexpage]

The system of \(3\) equations in \(2\) unknowns is

\begin{align*}
3 x_1 + 4.5 x_2 &= 1, \\
2x_1 + 1.2 x_2 &= -3.2, \\
-0.1 x_1 + 8.2 x_2 &= 1.5,
\end{align*}

which can be written as \( Ax = y \), where \( A \) is the \( 3 \times 2 \) matrix

\[
A = \left( \begin{array}{cc}
3 & 4.5 \\
2 & 1.2 \\
-0.1 & 8.2 \\
\end{array} \right),
\]

and \( y \) is the \( 3 \)-vector

\[
y = \left( \begin{array}{c}
1 \\
-3.2 \\
1.5 \\
\end{array} \right).
\]

The set of solutions turns out to be empty. Indeed, if we use the first two equations, and solve for \( x_1, x_2 \), we get \( x = (-2.8889, 2.1481) \), but then the last equation is not satisfied, since

\[-0.1 x_1 + 8.2 x_2 = 17.4741 \neq 1.5. \]