Answer
(0, 1, 2)
Work Step by Step
The question asks to find the solution to the system of equations.
Given:
1. $2x + 4y - z = 2$
2. $x + 2y - 3z = -4$
3. $3x - y + z = 1$
Add equations 1 and 3, multiply equation 3 by 3 and add it to equation 2
1. $2x + 4y - z = 2$
+ ($3x - y + z = 1$)
4. $5x + 3y = 3$
$x + 2y - 3z = -4$
+($9x - 3y + 3z = 3$)
5. $10x - y = -1$
Multiply equation 5 by 3, then add equation 5 and equation 4
$5x + 3y = 3$
+($30x - 3y = -3$)
$35x = 0$
$x = 0$
Solve for other variables
$5(0) + 3y = 3$
$3y = 3$
$y = 1$
$0 + 2(1) - 3z = -4$
$-3z = -6$
$z = 2$
Solution: (0, 1, 2)
