multiply the 2nd eqn. by 6
add 1st eqn to 2nd eqn, and to 3rd eqn
... this gives two eqns in y and z (x has been eliminated)
solve for y (or z) , then substitute back to find all unknowns
6x+5y-6z=-9
-x-y+3z=10
-6x-y+z=23
2 answers
Let's go for the y's
the 2nd: -x -y + 3z = 10
the 3rd: -6x - y + z = 23
subtract them:
5x + 2z = -13 **
the first as is: 6x + 5y - 6z = -9
5 times the 2nd: -5x -5y + 15z = 50
add those ...
x + 9z = 41 or x = 41- 9z ***
sub *** into **
5(41 - 9z) + 2z = -13
205 - 45z + 2z = -13
-43z = -218
z = 218/43
back in **
x = 41 - 9z = 41 - 9(218/43) = ....
now put that back into the original 2nd equation to find y
the 2nd: -x -y + 3z = 10
the 3rd: -6x - y + z = 23
subtract them:
5x + 2z = -13 **
the first as is: 6x + 5y - 6z = -9
5 times the 2nd: -5x -5y + 15z = 50
add those ...
x + 9z = 41 or x = 41- 9z ***
sub *** into **
5(41 - 9z) + 2z = -13
205 - 45z + 2z = -13
-43z = -218
z = 218/43
back in **
x = 41 - 9z = 41 - 9(218/43) = ....
now put that back into the original 2nd equation to find y