How do I find X Y and Z using these equations: 2x-y+2z=7 - x+2y-2z=-6 and - 2x+3y-4z=-9?

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