Let \(\alpha_1, \alpha_2\) and \(\beta_1, \beta_2\) be the roots of \(ax^2 + bx + c = 0\) and \(px^2 + qx + r = 0\) respectively. If the system of equations \(\alpha_1 y + \alpha_2 z = 0\) and \(\beta_1 y + \beta_2 z = 0\) has a non-trivial solution, then
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Use Vieta's formulas and the condition for non-trivial solutions.