Question 89175: I would appreciate any help with this. I don't know how to isolate the variable or which equation to work with first...
Solve:
5x-2y+2z=-24
x-3y-4z=33
3x+3y-2z=7
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Solve:
5x - 2y + 2z = -24
x - 3y - 4z = 33
3x + 3y - 2z = 7
:
Perform elimination operations, adding or subtracting to get rid of one of the
variables. Do this twice and you have two, 2 unknown equation which are easy to deal with.
:
There are some obvious ways you can do this in this problem to eliminate z:
Multiply the 3rd equation by -1 and Add all three.
5x - 2y + 2z = -24
x - 3y - 4z = 33
-3x - 3y + 2z = -7
---------------------adding eliminates z
3x - 8y + 0z = 2
:
Add the first & third equations:
5x - 2y + 2z = -24
3x + 3y - 2z = 7
------------------adding eliminates z again
8x + 1y = -17
:
Our two, 2 unknown equations:
3x - 8y = +2
8x + 1y = -17
:
Multiply the 2nd equation by 8 and add it to the 1st:
64x + 8y = -136
3x - 8y = +2
----------------adding eliminates y, solve for x:
67x + 0x = -134
x = -134/67
x = -2
:
Find y using 8x +y = -17
8(-2) + y = -17
-16 + y = -17
y = -17 + 16
y = -1
:
I'll let you find out what z is. Check all three solution in the original equations
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