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

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) (Show Source): You can put this solution on YOUR website!
2x � y + z = 7
x + 2y � 5z = -1
x � y = 6
------
x = 6+y
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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".
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Cheers,
Stan H.
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