Please lead me in the right direction. I am so confused and I have been working on this one problem for an hour. I have the answer, but I want to know how to get to it. The answer is (1,1,0)
Solve the system by elimination.
-2x+2y+3z=0; -2x-y+z=-3; 2x+3y+3z=5
Perfect setup, notice the coefficients of x are ±2, so nothing has to be done
add 2nd and last ---> 2y + 4z = 2 , #4
add 1st and last ---> 5y + 6z = 5 , #5
#4 times 5 ----->10y + 8z = 10
#5 times 2 ----> 10y + 12z = 10
subtract those two equations:
4z = 0
z = 0
in #4,
2y + 0 = 2
y = 1
in #1
-2x + 2 + 0 = 0
-2x = -2
x = 1
so
x=1
y=1
z=0
btw, this is just one of several ways to do this question.