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To solve the system of equations, we can use the substitution method. First, solve one of the equations for one of the variables. For example, we can solve the first equation for (x): (x = 5 - 2y). Then, substitute this expression for (x) into the other equation: (2(5 - 2y) - y = 1). This gives us (10 - 4y - y = 1), which simplifies to (-5y = -9). Dividing both sides by (-5), we get (y = 9/5). Substituting this value of (y) back into the first equation, we get (x + 2(9/5) = 5), which simplifies to (x = 1). Therefore, the solution to the system of equations is ((x, y) = (1, 2)).