Question 148374: How would I go about solving a system of equations with three equations and three variables.
4x-4y-z=38
x+4y-3z=6
-3x+2y-z=-14
Please explain step by step, I would appreciate it. Thank you.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! There are several methods to choose from.
One of them is the substitution method.
1.
2.
3.
You can use eq. 2 to come up with an expression for x in terms of y and z and substitute into eqs. 1 and 3.
2.
Now substitute into eq. 1,
1.
1.
1.
1.
1.
and eq. 3,
3.
3.
3.
3.
3.
3.
Now you've reduce from three variables to two variables.
1.
3.
You can again do a substitution to get y in terms of z.
From new eq. 1,
1.
1.
1.
Now substitute this value into new eq. 3.
3.
3.
3.
3.
3.
3.
Now go backwards and substitute to find y and then x.
3.
And finally x,
Your solution is therefore,
(x,y,z,)=(4,-4,-6)
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