Answer:
x=8/7, y=-25/7, z=15/7
Explanation:
x-y+2z=9 ==> equation 1
3x+y=z=2 ==> equation 2
2x-y+z=8 ==> equation 3
3x+y+z=2
+ (2x-y+z=8)
3x+2x + y+(-y) + z+z = 2+8 ==> add equation 2 and 3 to eliminate y
5x + 2z = 10 ==> equation 4
x-y+2z=9
- (2x-y+z=8)
x - 2x + (-y)-(-y) + 2z-z = 9-8 ==> subtract equation 1 and 3 to eliminate y
-x + 0 + z = 1 ==> Let's say -y=a. (-y)-(-y) = a-a = 0.
(-x + z = 1)*2 ==> multiply by 2 to get z to become 2z
-2x + 2z = 2 ==> equation 5
5x + 2z = 10
- (-2x + 2z = 2)
5x-(-2x) + 2z-2z = 10-2 ==> subtract equation 4 and 5 to solve for x
5x+2x = 8
7x = 8 ==> divide both sides by 7 to isolate x
x = 8/7
-2(8/7) + 2z = 2 ==> plugin x into equation 5 to solve for z
-16/7 + 2z = 2 ==> simplify
(-16/7 + 2z = 2)*7 ==> multiply the equation by 7 to eliminate fractions
-16 + 14z = 14
14z = 30 ==> add 16 on both sides to isolate z
z = 30/14 ==> divide each side by 14
z = 15/7 ==> simplify
2(8/7)-y+(15/7)=8 ==> plugin x = 8/7 and z = 15/7 into equation 3
16/7 - y + 15/7 = 8
(16/7 + 15/7 - y = 8)*7 ==> multiply the equation by 7 to remove fractions
16 + 15 - 7y = 56
31 - 7y = 56
-7y = 25 ==> subtract 31 on both sides to isolate y
7y = -25
y = -25/7
Answer: (x=8/7, y=15/7, z=-25/7)