Question

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

Answer 1

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