SOLUTION: How would you go about finding the solution to this system of three equations in three variables? 2x – y + z = 7 x + 2y – 5z = -1 x – y = 6

Algebra ->  Equations -> SOLUTION: How would you go about finding the solution to this system of three equations in three variables? 2x – y + z = 7 x + 2y – 5z = -1 x – y = 6      Log On


   

Question 1072213: How would you go about finding the solution to this system of three equations in three variables?


2x – y + z = 7
x + 2y – 5z = -1
x – y = 6
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2x – y + z = 7
x + 2y – 5z = -1
x – y = 6
------
x = 6+y
-----
Substitute for "x" in the 1st and the 2nd equation
to get two equations in y and z.
--------------------------------
12+2y-y+z = 7
6+y + 2y - 5z = -1
--------
y + z = -5
3y - 5z = -7
--------
Modify::
3y + 3z = -15
3y - 5z = -7
-------
Subtract and solve for "z":
8z = 8
z = 1
----
Then solve for "y".
Then solve for "x".
------------
Cheers,
Stan H.
------------