Question

3x-y+z=-3
-2x+y-2z=8
-4x+3y-z=6

Answer 1

$z = - 3x + y - 3$

$y = 2x + 2z + 8$

$- 4x + 3(2x + 2z + 8) - ( - 3x + y - 3) = 6 \\ - 4x + 6x + 6z + 24 + 3x - z + 3 = 6 \\ - 4x + 6x + 3x + 6z - z = 6 - 24 - 3 \\ 5x + 5z = - 21 \\ x = z - \frac{21}{5}$

$y = 2(z - \frac{21}{5} ) + z + 8 \\ y = 2z - \frac{42}{5} + z + 8 \\ y = 3z - \frac{2}{5}$

$z = 3(z - \frac{21}{5} ) + (3z - \frac{2}{5} ) - 3 \\ z = 3z - \frac{91}{5} + 3 z - \frac{2}{5} - 3 \\ z = 6z - \frac{93}{5} - 3 \\ - 5z = - \frac{108}{5} \\ z = \frac{108}{25}$