Answer
(1, 1, 2)
Work Step by Step
The question asks to find the solution to the system of equations.
Given:
1. $x + y + 2z = 6$
2. $2x + 5z = 12$
3. $x + 2y + 3z = 9$
Multiply equation 1 by 2, then subtract equation 3 from the result of equation 1
1. $2x + 2y + 4z = 12$
-($x + 2y + 3z = 9$)
4.$x + z = 3$
Double equation 4, then subtract the result from equation 2
2. $2x + 5z = 12$
- ($2x + 2z = 6$)
$3z = 6$
$z = 2$
Solve for other variables
$2x + 5(2) = 12$
$2x = 2$
$x = 1$
$(1) + y + 2(2) = 6$
$y = 1$
Solution: (1, 1, 2)
