Question 313259
2x+ y-3z=-12
3x-2y-z= 3
-x+5y+2z=-3
-------------
To use elimination, pick one of the variables to eliminate.
I'll eliminate z
Multiply eqn 2 by 2 and add it to eqn 3.
Then multiply eqn 2 by 3 and subtract it from eqn 1
-------------
3x-2y-z= 3 x2 --> 6x-4y-2z = 6
-x+5y+2z=-3
6x-4y-2z = 6
------------ Add
5x + y = 3  Eqn A
----------
2x+ y-3z=-12
3x-2y-z= 3 x3 --> 9x-6y-3z = 9
2x+ y-3z=-12
9x-6y-3z = 9
------------ Subtract
-7x+5y = -21 Eqn B
--------------------
Now eqns A and B are in x and y only
-7x+5y = -21 Eqn B
25x+5y = 15 Eqn A times 5
------------ Subtract
-32x = -36
x = 9/8
--------
Sub for x into Eqn A or B
5*(9/8) + y = 3
y = 3 - 45/8
y = -21/8
----------
Sub for x and y into eqn 2 (or any of the original 3)
3x-2y-z= 3
3*(9/8) - 2*(-21/8) - z = 3
z = -3 + 27/8 + 42/8 = -3 + 69/8
z = 45/8