The straight lines x+2y-9=0, 3x+5y-5=0, and a | vedclass

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(D) The condition for the lines $x+2y-9=0$, $3x+5y-5=0$, and $ax+by-1=0$ to be concurrent is that the determinant of their coefficients must be zero:$

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$(a, b)$

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(D) The condition for the lines $x+2y-9=0$, $3x+5y-5=0$, and $ax+by-1=0$ to be concurrent is that the determinant of their coefficients must be zero:$\left|\begin{array}{ccc}1 & 2 & -9 \ 3 & 5 & -5 \ a & b & -1\end{array}ight|=0$Expanding along the third row:$a(-10 + 45) - b(-5 + 27) + (-1)(5 - 6) = 0$$35a - 22b + 1 = 0$This equation implies that the point $(a, b)$ satisfies the equation $35x - 22y + 1 = 0$. Therefore, the line $35x - 22y + 1 = 0$ passes through the point $(a, b)$.

The straight lines $x+2y-9=0$, $3x+5y-5=0$, and $ax+by-1=0$ are concurrent if the straight line $35x-22y+1=0$ passes through the point

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