#1**+1 **

START this way:

Multiply FIRST equation by -2

then add to equation 3

this will allow you to solve for z...........continue on your own and see if you can find x and y

ElectricPavlov May 25, 2019

#2**+1 **

First....there is no "set" way of doing this.....using EP's idea we have

-2x + 2y - 6z = -12

2x - 2y + 5z = 9 add these and we get

-z = -3

z = 3

Now using the first equation we have that

x - y + 3(3) = 6

x - y + 9 = 6 subtract 9 from both sides

x - y = -3

So now we have two equations to work with

x - y = - 3 multiply through by - 1 ⇒ -x + y = 3 (4)

x - 2y = 5 (5)

Add (4) and (5) and we have that

-y = 8 ⇒ y = - 8

And using (4) to find x -x + (-8) = 3 add 8 to both sides

-x = 11

x = -11

So

{x, y, z} = { -11, -8, 3 }

These take some real practice, GM.......also......easy to make mistakes.....be careful !!!

CPhill May 25, 2019