Question 215902
Find a point that solves all equations algebraically. The equations are:
8x+2y-z=-25
3x-3y+5z=10
-5x+6y-2z=17 
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Eliminate z
40x + 10y - 5z = -125 (1st eqn times 5)
+3x - 3y + 5z = 10
------------------- Add
43x + 7y = -115 Eqn A
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16x + 4y - 2z = -50 (1st eqn times 2)
-5x + 6y - 2z = 17
------------------- Subtract
21x - 2y = -67 Eqn B
147x - 14y = -469 times 7
+86x + 14y = -230 (eqn A times 2)
------------------ Add
233x = -699
x = -3
-------   x is done.
Sub for x into Eqn B
-63 - 2y = -67
y = 2 ------- That's y
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Sub x & y into 8x+2y-z=-25
-24 + 4 - z = -25
z = 5
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There's a good chance these are correct, you can check.  If I made a mistake, just use the same method and correct it.
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It's an error-prone business.  The best way to do this is to use Excel and determinants.