SOLUTION: solutions of three equations in three variables x+y+z=4 2x+y-z=1 2x-3y+z=1 i want to eliminate z first so i believe i take equations 2 & 3 and add them and my result is:

Question 796942: solutions of three equations in three variables
x+y+z=4
2x+y-z=1
2x-3y+z=1
i want to eliminate z first so i believe i take equations 2 & 3 and add them and my result is:
2x+y-z=1
+ 2x-3y+z=1
------------------
4x-2y=2

what do i do from here can someone help me?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x+y+z=4
2x+y-z=1
2x-3y+z=1
i want to eliminate z first so i believe i take equations 2 & 3 and add them and my result is:
2x+y-z=1
+ 2x-3y+z=1
------------------
4x-2y=2

what do i do from here can someone help me?
=========================
Add 1 & 2, then you have 2 eqns in x & y.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You can also add equations 1 and 2, eliminating z from those two as well. That will give you a second equation in x and y only. That leaves you with a 2X2 system. As it happens, you will then be able to add the two 2-variable equations to eliminate y. From there you solve the single variable equation in x, substitute the value for x into either of the 2-variable equations, solve for y, then substitute x and y into any one of the original equations and solve for z.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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