Question 186542
2x + 3y + 2z = 1
2x - 3y + 2z =-1
4x + 3y - 2z = 4
:
Use elimination with subtraction on 1st two equations
2x + 3y + 2z = 1
2x - 3y + 2z =-1
------------------ 
0x + 6y + 0z = 2
6y = 2
y = {{{2/6}}} = {{{1/3}}}
:
Add the last two equations, eliminate y & z, find x
2x - 3y + 2z =-1
4x + 3y - 2z = 4
------------------
6x + 0y + 0z = 3
6x = 3
x = {{{3/6}}} = {{{1/2}}}
:
Using the 1st equation, substitute for x & y, to find z
2({{{1/2}}}) + 3({{{1/3}}}) + 2z = 1
1 + 1 + 2z = 1
2z = 1 - 2 
z = {{{-1/2}}}
;
;
You can check the solutions in the 2nd and 3rd equation