Inductive Proof (+linear equation in four variables)

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I'm trying to prove by induction that \forall n \geq 5, \exists m_1, m_2 \in \mathbb{N} such that n = 2m_1 +3m_2.I've done the base case, and the inductive step boils down to showing that \exists m_1 \prime m_2 \prime such that 2m_1 +3m_2 +1 = 2m_1 \prime +3m_2 \prime. Maybe I'm forgetting something from grade school algebra, but I have no idea how to solve for m_1 \prime, m_2 \prime. I've plugged it into wolfram alpha [http://www.wolframalpha.com/input/?i=2*x_1+3*x_2+++1+=+2*y_1+++3*y_2] and got solutions (all I care about is the case n =1 for the integer solutions wolfram gives) but I want to know how to arrive there.
 
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