Systems of equations

Algebra Level 5

\[\begin{align} 17x + sy + tz = 0\\ rx + 34y + tz = 0\\ rx + sy + 87z = 0 \end{align}\]

Let \(r, s, t, x, y,\) and \(z\) be real numbers with \(r \neq 17\) and \(x \neq 0\) that satisfy the system of equations above.

Compute \(\dfrac {17}{17 - r}+\dfrac {34}{34 - s} + \dfrac {87}{87 - t}\).

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