substitution problem?

Question

-2x + 2y - 3z = 22

2x + 2y + 3z = -34

-4x + 8y - 6z = 32

Answer 1

-2x + 2y - 3z = 22

2x + 2y + 3z = -34

-4x + 8y - 6z = 32


Adding the first two equations, we get

-2x + 2y - 3z + 2x + 2y + 3z = 22 + (-) 34

4y = 22 - 34 = -12

y = -12/4 = -3

Substituting y in the first equation, we get

-2x + (-) 6 - 3z = 22

2x - 3z = -28

Multiplying by 2 we get

4x - 6z = -56

The third equation can be written as

-4x +8 (-3) - 6z = 32

-4x - 24 - 6z = 32

-4x - 6z = 32 + 24 = 56

We add this and the other equations. We write both for clarity:

-4x - 6z = 56

4x - 6z = - 56

We get -12z = 0 and z = 0

So, we have 4x = - 56 and x = - 56/4 = - 14


So, x = - 14, y = -3 and z = 0

Answer 2

-2x + 2y - 3z = 22
2x + 2y + 3z = -34
-4x + 8y - 6z = 32

Using the first 2 equations, adding them together gives
4y = -12 so y = -3

The equations then become:
-2x - 6 -3z = 22 .......... -2x -3z = 28
2x - 6 +3z = -34 ........... 2x + 3z = -28
-4x -24 -6z = 32 ........... -4x -6z = 56

These are all multiples of each other, and show that x and z are on a line in the plane with multiple possible values of (x,z), such as (-14,0), (-2, -8), (0, -28/3)

-------------
EDIT: Swamy, you have dropped a negative sign when subbing y=(-3) back into the first equation... If you were switching all the signs, then 3z should be positive in that line

Answer 3

You have to make x the subject of y and z
then make y the subject of x and z
so on... Sub them in
Do it step by step
this is going to take up more then one page of the paper.
Work hard!

Answer 4

use the 1st two eqtns to get:
4y=22
y=11/2

Then use the last two to get Z &X