SOLUTION: Solve the following system of equations algebraically for all values of x,y,and z x-2y+3z=30 4x+3y-2z=53 -6x+8y-9z=-97 x=? y=? z=?

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following system of equations algebraically for all values of x,y,and z x-2y+3z=30 4x+3y-2z=53 -6x+8y-9z=-97 x=? y=? z=?      Log On


   

Question 1106202: Solve the following system of equations algebraically for all values of x,y,and z
x-2y+3z=30
4x+3y-2z=53
-6x+8y-9z=-97
x=?
y=?
z=?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x-2y%2B3z=30
2.4x%2B3y-2z=53
3.-6x%2B8y-9z=-97
Multiply eq. 1 by 4 and subtract from eq. 2,
4x-8y%2B12z-4x-3y%2B2z=120-53
4.-11y%2B14z=67
Multiply eq. 1 by 6 and add to eq. 3,
6x-12y%2B18z-6x%2B8y-9z=180-97
5.-4y%2B9z=83
Multiply eq. 4 by 4 and eq. 5 by -11 and add them together,
-44y%2B56z%2B44y-99z=268-913
-43z=-645
z=15
Now back substitute and solve for y and then x.