$$\begin{array}{rcrcrcr} x & - & 2y & + & 3z & = & 7 \\\ 2x & + & y & + & z & = & 4 \\\ -3 x & + & 2y &- &2z & = & -10 \end{array}$$
I have no idea how to do this and my math book is just telling me to do it, and explains nothing. I have a problem containing 3 equations with 3 variables. What do I do? I tried to solve for x and y and then find z but that didn't work and I got the wrong answer. What do I do? My book tells me to "Multiply each side of equation by -1 and add the result to equation 2, also add equations 2 and 3" I have no idea what this means or why they do it, it is never explained in this book anywhere and they seem like completely arbirtrary number not dependent upon anything, like the author is doing it for fun.