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.