Question

Solve the following system:
4x-y+z=6
2x+y+2z=3
3x-2y+z=3

Find the values for x, y, and z

Answer 1

add the first and second
6x + 3z = 9 -----> 2x + z = 3 , #4

double the 2n
4x + 2y + 4z = 6
add that to the third
7x + 5z = 9 , #5

#4 times 5 ----> 10x + 5z = 15
#5 -----------> 7x + 5z = 9
subtract them:
3x = 6
x = 2

back in #4 , 4 + z = 3 , z = -1
back in #2
4 + y - 2 = 3
y = 1

x=2
y=1
z= -1

note:
I used elimination. My particular series of steps is not unique, there are many ways to solve the above.
Mine is not necessarily the easiest way.