If the values of $x, y,$ and $z$ satisfy the equations
\[
2x - 3y + 2z + 15 = 0, 3x + y - z + 2 = 0, x - 3y - 3z + 8 = 0
\]
simultaneously are $\alpha, \beta,$ and $\gamma$ respectively, then
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To find relations between parameters satisfying simultaneous equations, try adding, subtracting, or multiplying equations to eliminate variables and find relations.
Given three linear equations, their solutions are related to $\alpha, \beta, \gamma$. By manipulating and substituting the values or comparing coefficients, we get the relation $2\alpha + \beta = \gamma$.