(Solved): It was shown in the above examples that the following \( 2 \times 2 \) linear system has an infini ...

It was shown in the above examples that the following \( 2 \times 2 \) linear system has an infinite number of solutions: 1) \( 2 x_{1}-x_{2}=3 \) 2) \( -8 x_{1}+4 x_{2}=-12 \) The solutions are given by: \[ \begin{array}{l} x_{1}-\frac{1}{2} r+\frac{3}{2} \\ x_{2}=r \end{array} \] where \( r \in \) (i.e., \( -\infty