Question

I need help showing step by step and answer.

Answer 1

Answer: x=3 y=-1 z=2

Explanation:

`\displaystyle\\\left\{\begin{array}{ccc}x+y-z=0\ \ \ \ (1)\\2x+y-2z=1\ \ (2)\\3x-4z=1\ \ \ \ \ \ \ (3)\end{array}\right`

Multiply equation (1) by -2:

`\displaystyle\\\left\{\begin{array}{ccc}-2x-2y+2z=0\ \ \ \ (1)\\2x+y-2z=1\ \ (2)\\3x-4z=1\ \ \ \ \ \ \ (3)\end{array}\right`

Add equations (1) and (2):

`- y=1`

Multiply both parts of the equation by -1:

`y=-1`

Substitute the value of y into equation (2):

`2x+(-1)-2z=1\\2x-1-2z=1\\2x-1-2z+1=1+1\\2x-2z=2`

Divide both parts of the equation by 2:

`x-z=1\ \ \ \ (4)`

Multiply both parts of the equation by -3:

`-3x+3z=-3\ \ \ \ (5)`

Add equations (3) and (5):

`-z=-2`

Multiply both parts of the equation by -1:

`z=2`

Substitute the value of z into equation (4):

`x-2=1\\x-2+2=1+2\\x=3`