Too many unknowns!

Algebra Level 4

a1x1+a2x2+a3x3+a4x4=1432a7x1+a6x2+a5x3+a8x4=2341a11x1+a12x2+a13x3+a10x4=3412a17x1+a16x2+a15x3+a14x4=4321\large{\begin{aligned} \color{#D61F06}{a_1x_1 + a_2x_2+a_3x_3+a_4x_4} &= \color{#D61F06}{1432} \\ \color{#20A900}{a_7x_1 + a_6x_2+a_5x_3+a_8x_4} &= \color{#20A900}{2341} \\ \color{#3D99F6}{a_{11}x_1 + a_{12}x_2+a_{13}x_3+a_{10}x_4} &= \color{#3D99F6}{3412} \\ \color{magenta}{a_{17}x_1 + a_{16}x_2+a_{15}x_3+a_{14}x_4} &= \color{magenta}{4321} \end{aligned} }

Suppose a1,a2,a3,,a15,a16,a17a_1 , a_2 , a_3, \ldots, a_{15} , a_{16} , a_{17} form an arithmetic progression such that a9=257a_9=257 . Find the value of x1+x2+x3+x4\color{#624F41}{\lfloor x_1 + x_2+x_3+x_4 \rfloor}.

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