Solution MISLE.C22 Robert Beezer
Represent each of the two systems by a vector equality, $A\vect{x}=\vect{c}$ and $A\vect{y}=\vect{d}$. Then in the spirit of Example SABMI, solutions are given by \begin{align*} \vect{x}&=B\vect{c}=\colvector{8\\21\\-5\\-16}& \vect{y}&=B\vect{d}=\colvector{5\\10\\0\\-7} \end{align*} Notice how we could solve many more systems having $A$ as the coefficient matrix, and how each such system has a unique solution. You might check your work by substituting the solutions back into the systems of equations, or forming the linear combinations of the columns of $A$ suggested by Theorem SLSLC.