Step 1 :First, we rewrite the system of equations in standard form: \begin{align*} -2x + y &= -1, \\ 2x + y &= 1. \end{align*}
Step 2 :Next, we add the two equations together: \begin{align*} (-2x + y) + (2x + y) &= -1 + 1, \\ 2y &= 0, \\ y &= 0. \end{align*}
Step 3 :Substitute \(y = 0\) into the first equation: \begin{align*} -2x + 0 &= -1, \\ -2x &= -1, \\ x &= 0.5. \end{align*}
Step 4 :Thus, the solution to the system of equations is \(\boxed{(0.5, 0)}\).