In Problems 1 through 16, apply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. For each problem, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.

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x₁ = x₁ - 2x2, x₂ = 2x₁ + x2; x₁ (0) = 0, x2 (0) = 4