Answer
$$2x+5z=-12 \\ y-2z=7 \\ 6x+3y=2$$
Work Step by Step
In order to write a matrix that would solve a linear equation, we would write the coefficients of each variable in their own column. Thus, we reverse the process to find:
$$2x+5z=-12 \\ y-2z=7 \\ 6x+3y=2$$