Question 968954: I am having trouble trying to solve this problem. I would be very grateful if you could explain to me the steps in finding the answers.
Solve each system using any method: [referring to substitution and elimination]
3x-2y-3z=0
x-3y+z=10
2x+2y-4z=-10
Thank you so much.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 3x - 2y - 3z = 0
x - 3y + z = 10
2x + 2y -4z =-10
:
Multiply the 1st equation by -1 to change the signs
-3x + 2y +3z = 0
x - 3y + z = 10
2x + 2y -4z =-10
-------------------Addition eliminates x and z
0 + y + 0 = 0
y = 0
Back to the 1st equation replace y with 0 and you have
3x - 3z = 0
3x = 3z
divide both sides by 3, therefore
x = z
Back to the 3rd original equation, replace z with x and y with 0
2x - 4x = - 10
-2x = -10
x = -10/-2
x = +5
Therefore
z = 5 also
;
We have x=5, y=0, z=5
:
See if that checks out in the 2nd original equation
x - 3y + z = 10
replace x with 5, y with 0, z with 5
5 - 0 + 5 = 10
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