Answer
(3, 1, 0)
Work Step by Step
The question asks to find the solution to the system of equations.
Given:
1. $x - 2y + 3z = 1$
2. $x - 3y - z = 0$
3. $2x - 6z = 6$
Solve for x in equation 3
$2x = 6z + 6$
$x = 3z + 3$
Substitute x in equation 1 and 2
$(3z + 3) - 2y + 3z = 1$
4. $6z - 2y = -2$
$(3z + 3) - 3y - z = 0$
5. $2z - 3y = -3$
Multiply equation 5 by 3, subtract the result from equation 4
$6z - 2y = -2$
-($6z - 9y = -9$)
$7y = 7$
$y = 1$
Solve for other variables
$2z - 3 = -3$
$2z = 0$
$z = 0$
$x = 3 (0) + 3$
$x = 3$
Solution: (3, 1, 0)
