Answer:
x=4/5, y=1/5, z=14/5
or
using decimals
x=0.8, y=0.2, z= 2.8
Step-by-step explanation:
2x-y+2z=7 (1)
-x+2y-2z=-6 (2)
2x+3y-4z=-9 (3)
1) Add equations (1) and (2)
2x-y+2z=7
-x+2y-2z= - 6
x + y = 1 (equation 5)
2) Multiply equation (2) by - 2
-x+2y-2z= - 6 / *(-2)
2x - 4y+4z = 12 (equation 4)
3) add equation (4) and (3)
2x - 4y+4z = 12
2x +3y -4z= - 9
4x - y = 3 (equation 6)
4) Add equation (5) and equation (6) to find x
x + y = 1
4x - y = 3
5x = 4
x = 4/5
5) Use equation 5 to find y
x+y = 1, x=4/5
4/5+y=1
y=1/5
6) Use equation (1) to find z
2x-y+2z=7 , x=4/5, y=1/5
2*4/5 - 1/5 +2z =7
8/5-1/5 +2z = 7
7/5 + 2z = 7
2z = 7- 7/5
2z = 35/5 - 7/5
2z = 28/5
z =14/5
