solve the following systems?

Question

2x+y-3z= -14
x-3y+4z=22
3x+2y+z=0

Answer 1

Add the second equation to the first to eliminate y:

6x + 3y - 9z = -42
x - 3y + 4z = 22
- - - - - - - - - - - - -
7x - 5z = -20

And to the third equation:

2x - 6y + 8z = 44
9x + 6y + 3z = 0
- - - - - - - - - - - - -
11x + 11z = 44

And just to make it easier, divide both sides of that equation by 11:

x + z = 4

Then multiply by 5 and add to the other 2-variable equation above:

5x + 5z = 20
7x - 5z = -20
- - - - - - - - - -
12x = 0
x = 0

Therefore:

0 + z = 4
z = 4

And then:

3(0) + 2y + 4 = 0
2y = -4
y = -2

So the solution is (0, -2, 4).

Answer 2

2x+y-3z= -14
x-3y+4z=22
3x+2y+z=0

____│_2__1_-3_│
DO=│_1_-3__4_│ = -6+12-6 –27-16-1= -44;
____│_3__2__1_│

DO ≠ 0, OK! then continue;

____│-14_1_-3_│
DX=│22_-3__4_│ = 42+0-132 -0+112-22= 0;
____│_0__2__1_│

____│_2_-14__-3_│
DY=│_1__22__4_│ = 44-168+0 +198+14-0= 88;
____│_3__0___1_│

____│_2__1_-14│
DZ=│_1_-3__22│ = -0+66-28 –126-88-0= -176;
____│_3__2__0_│

x=DX/DO =0;
y=DY/DO =-88/44 =-2;
z=DZ/DO =176/44=4;