1. The problem statement, all variables and given/known data In Exercises 49 and 50, find values of a, b, and c(if possible) such that the system of linear equations has (a) a unique solution, (b) no solution, and (c) an infinite number of solutions. 49. [itex]x+y ~ = 2[/itex] [itex]~y+z =2[/itex] [itex]x+ ~ z =2[/itex] [itex]ax + by + cz=0[/itex] 2. Relevant equations 3. The attempt at a solution I immediately recognized this system as one consisting of planes. Hence, wouldn't it be impossible for there to exist a unique solution, as my geometric intuition of the situation ?