SOLUTION: Solve by substitution or elimination: 3x-4y+2z=-2 5x-y+3z=1 x+y-z=-5

Question 162861: Solve by substitution or elimination:
3x-4y+2z=-2
5x-y+3z=1
x+y-z=-5
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
3x-4y+2z=-2
5x-y+3z=1
x+y-z=-5
=============
I'll go ahead and use elimination;
Add 2 equations together to eliminate the y;
5x-y+3z=1
x+y-z=-5
----------
6x+2z=-4
=============
now add together 2 other equations to eliminate the y;
3x-4y+2z=-2
x+y-z=-5 - multiply this equation by 4 so the y will eliminate;
-----------
4(x+y-z=-5)
4x+4y-4z=-20
=============
Now add the 2 equations;
3x-4y+2z=-2
4x+4y-4z=-20
-------------
7x-2z=-22
================
Now add the new equations together to eliminate a variable;
6x+2z=-4
7x-2z=-22
---------
13x=-26
x=-2
==============
Now we have what x equals, so we plug that into the equations then add them together to eliminate another variable;
5x-y+3z=1
x+y-z=-5
==============
-10-y+3z=1
-2+y-z=-5
----------
-12+2z=-4
2z=8
z=4
===========
Now that we have both x and z we can plug those into any equation and find y;
x+y-z=-5
-2+y-4=-5
-6+y=-5
y=1
=============
Check;
-2+1-4=-5
-1-4=-5
-5=-5
check;
5x-y+3z=1
-10-1+12=1
-11+12=1
1=1
:)

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