Steps:
isolate " x " for -2x + 2y + 3z = 0 ; x = - ( - 3z - 2y ) / 2
Subsititute : x = - ( - 3z - 2y ) / 2
- 2 * ( - ( - 3z - 2y ) / 2 ) - y + z = - 3
2 * ( - ( - 3z - 2y ) / 2 ) + 3y + 3z =5
isolate " z " for : - 2 ( - ( - 3z - 2y ) / 2 ) - y+ z = - 3 ; z = - ( - 3 + 3y / 2 )
subsititute z = - ( - 3 + 3y / 2 ) :
2* ( - ( -3* ( - ( - 3 +3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5
isolate y for 2 ( -( - 3 ) - 3 + 3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5
y = 1
for z = - ( - 3+ 3y ) / 2
subsititute y = 1
z = - ( - 3 + 3 * 1 ) / 2
z = 0
For x = - ( - 3z - 2y ) / 2
subsititute y = 1
subsititute z = 0
x = - ( - 3 *0 - 2 * 1 ) / 2
x = 1
x = 1 , y = 1 , z = 0
