1. The problem statement, all variables and given/known data A system of two equations with 3 variables is given. x + 2y +z = 1 3x - 4y = 2 calculate a thrird equation and add it to the system. the resulting system must have one and only one solution. 2. Relevant equations 3. The attempt at a solution my guess is that I must solve the matrix x + 2y +z = 1 3x - 4y = 2 ax + by+ cz =d for x, y, z but I have no idea how to show that this system has only one solution. I really need help with this please. Any advice is welcome, thanks in advance.