Linear systems of equations arise frequently in applications. They are usually solved by Gaussian Elimination and Backward Substitution. When working by hand it is crucial to organize the computation in a clear way that lets you check your calculations so far. A linear system may have none, one, or infinitely many solutions.
Solve the linear system $$\begin{array}{cccc} 4x & -y & = & 3 \\ 2x &+y & = & 5 \\ \end{array}$$
$x=$ and $y=$ .