Three lines 3x - y = 2,5x + ay = 3,and 2x + y | vedclass

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(D) For three lines $a_1x + b_1y + c_1 = 0$,$a_2x + b_2y + c_2 = 0$,and $a_3x + b_3y + c_3 = 0$ to be concurrent,the determinant of their coefficients

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$-2$

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(D) For three lines $a_1x + b_1y + c_1 = 0$,$a_2x + b_2y + c_2 = 0$,and $a_3x + b_3y + c_3 = 0$ to be concurrent,the determinant of their coefficients must be zero:$\begin{vmatrix} 3 & -1 & -2 \ 5 & a & -3 \ 2 & 1 & -3 \end{vmatrix} = 0$Expanding the determinant along the first row:$3(-3a - (-3)) - (-1)(-15 - (-6)) + (-2)(5 - 2a) = 0$$3(-3a + 3) + 1(-9) - 2(5 - 2a) = 0$$-9a + 9 - 9 - 10 + 4a = 0$$-5a - 10 = 0$$-5a = 10$$a = -2$

Three lines $3x - y = 2$,$5x + ay = 3$,and $2x + y = 3$ are concurrent. Find the value of $a$.

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