Answer
The solution is $(-\frac{4}{3},-\frac{17}{3},\frac{26}{3})$
Work Step by Step
Rewrite the system as a linear system in two variables.
Add Equation 1 and Equation 3.
$ 2x - 5y- z = 17$
$-4x + 6y + z=-20$
__________________________
$-2x+y=-3$
$ 6x - 15y - 3z = 51$
$x + y + 3z = 19$
__________________________
$7x-14y=70$
Solve the new linear system for both of its variables.
$-2x+y=-3$
$7x-14y=70$
Add $14$ times new Equation 1 to new Equation 2:
$-28x+14y=-42$
$7x-14y=70$
___________________
$-21x=28$
$x=-\frac{4}{3}$
Solve for y: $7(-\frac{4}{3})-14y=70$
$y=-\frac{17}{3}$
Solve for z: $-\frac{4}{3}-\frac{17}{3}+3z=19$
$z=\frac{26}{3}$
The solution is $(-\frac{4}{3},-\frac{17}{3},\frac{26}{3})$.
