SOLUTION: Find a point that solves all equations algebraically. The equations are: 8x+2y-z=-25 3x-3y+5z=10 -5x+6y-2z=17 I have tried several different times to solve by adding and subt

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
I have tried several different times to solve by adding and subtracting the equations to get an equation with two solutions, then add and subtract those to solve for one variable and then be able to fill in a two variable equation to get the next variable and finally stick it all in an original equation to get the last variable. I tried substitution. I end up with really big, really ugly answers that, when plugged in, do not add up right. I don't know what else to try. Thank you for your help.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find a point that solves all equations algebraically. The equations are:
8x+2y-z=-25
3x-3y+5z=10
-5x+6y-2z=17
-----------
Eliminate z
40x + 10y - 5z = -125 (1st eqn times 5)
+3x - 3y + 5z = 10
------------------- Add
43x + 7y = -115 Eqn A
-------------
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
---------------
Sub x & y into 8x+2y-z=-25
-24 + 4 - z = -25
z = 5
----------------
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.

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