If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:
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Look at the coefficients of the given line $22x - 35y = 1$ and the obtained relation $22b - 35a = 1$. By matching variables, $x = b$ and $y = a$, yielding the point $(b, a)$ instantly.