Answer
(-1, 1, 2)
Work Step by Step
The question asks to find the solution to the system of equations.
Given:
1. $x - y + 2z = 2$
2. $3x + y + 5z = 8$
3. $2x - y - 2z = -7$
Add equations 1 and 2, equations 2 and 3
$x - y + 2z = 2$
+($3x + y + 5z = 8$)
4. $4x + 7z = 10$
$3x + y + 5z = 8$
+($2x - y - 2z = -7$)
5. $5x + 3z = 1$
Multiply equation 4 by 5 and equation 5 by 4, then subtract 5 from 4
$20x + 35z = 50$
-($20x + 12z = 4$)
$23z = 46$
$ z = 2$
Solve for other variables
$20x + 35(2) = 50$
$20x = -20$
$x = -1$
$(-1) - y + 2(2) = 2$
$-y = -1$
$y = 1
Solution: (-1, 1, 2)
