1. The problem statement, all variables and given/known data Find all solutions of the linear system x + 2y + 3z = a x + 3y + 8z = b x + 2y + 2z = c where a,b, and c are arbitrary constants. 2. Relevant equations 3. The attempt at a solution Using elimination, I managed to set the coefficients on the diagonal equal to 1, which then allowed me to solve for z, which was z = -c + a. Substituting z into the other equations to obtain x and y, I ended up with the following solution: x= -6a - 2b + 13c y = b + 4a -5c z = a - c I was wondering if my method of solving is valid, and if the answer I obtained seems reasonable. Thanks.