SOLUTION: x+y+z=-7 2x+5y+2z=-26 -x+9y-3z=-21 what are the variables?

Question 29316: x+y+z=-7
2x+5y+2z=-26
-x+9y-3z=-21
what are the variables?
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
x+y+z=-7
2x+5y+2z=-26
-x+9y-3z=-21
Solve this by elimination;
first take two of the equations and add them together to eliminate one of the variables;
x+y+z=-7
-x+9y-3z=-21
------------
10y-2z=-28
Now start over with two of te other equations and eliminate the same variable.
2x+5y+2z=-26
-x+9y-3z=-21
since two of the variables don't cancel each other out, you need to mumltiply one of the equations by a number so you can have a variable cancel, we willmultiply the second equation by 2;
2x+5y+2z=-26
-2x+18y-6z=-42
---------------
23y-4z=-68
Now add this equation with the other;
23y-4z=-68
(-2)10y-2z=-28
-----------
23y-4z=-68
-20y+4z=56
----------
3y=-12
y=-4
Now plug -4 into one of the other equations to get z;
10(-4)-2z=-28
-40-2z=-28
-2z=12
z=-6
x+(-4)+(-6)=-7
x-10=-7
x=3
hope you understand, I know there are alot of steps
=)
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