I came along with the following exercise that I developed poorly. May anybody give me some light? See:
How to find a solution involving $a$, $b$, $c$ to make the following system consistent? Find the solutions when possible.
$$x + y + z + t = a$$ $$5y + 2z + 4t = b$$ $$3x - 2y + z - t = c$$
Well. First I tried to reduce the system to the reduced row echelon form, with not very success. What I got is:
$$x - \frac{2}{5}t = \frac{5a - b}{5}$$ $$y + \frac{2}{5}t = \frac{-c + 3a}{5}$$ $$z + t = \frac{c - 3a + b}{5}$$
I thought it would help, but I don't know how to resume the exercise.
Any tips?
Thank you.