Determine which of A-D form a solution to the given system for any choice of the free parameter $s_1$. List all letters that apply. If there is more than one answer, type them as a comma separated list.

$$\begin{array}{rcrcrcr}-5 x_1 & + & 3 x_{2} & - & 12 x_{3} & = & 27 \\-2 x_1 & + & x_{2} & - & 5 x_{3} & = & 11\end{array}$$

HINT: All of the parameters of a solution must cancel completely when substituted into each equation.

    A. $\left(-\left(6+3s_1\right),-\left(1+s_1\right),s_1\right)$

    B. $\left(-\frac{4-2s_1}{15},s_1,\frac{3+s_1}{36}\right)$

    C. $\left(3s_1-3,s_1,-\left(1+s_1\right)\right)$

    D. $\left(6-s_1,5-s_1,s_1\right)$

Answer(s):