Linear Algebra Systems of Equations I'm just starting out, so please bear with me. 
While solving systems of equations in linear algebra, can you straight-up add, if two factors cancel?
My problem: 
$$x_1 + 3x_2 -x_3 +x_4 +2x_5 = 2,$$
$$2x_1 -x_2 +x_3 -x_4 + x_5 = -2,$$
$$4x_1 +2x_2 +2x_3 -x_4 -x_5 = 0.$$
I thought that I could multiply 1 by equation 2, and then add that to equation 1, which would cancel both the $x_3$ and the $x_4$ factors for that line. Is that permissible? My book says to begin with the $x_1$ factors, so I'm not sure. Thanks.

What you suggest is just fine. But doing what your book suggests is not a bad idea either. Since you have three equations and five unknowns, you will only be able to solve for three of the variables (at most) in terms of the other two anyway.
