Question 401924: 2x-3y+z=5
x+3y+8z=22
3x-y+2z=12
showsteps also please
system of equations in three variables
Answer by sofiyac(983)   (Show Source):
You can put this solution on YOUR website! 1)****2x-3y+z=5
2)****x+3y+8z=22
3)****x-y+2z=12
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Add equations (eq) 1 and 2.
3x+9z=27 %%%%%%
Then multiply eq 3 by 3
3x-3y+6z=36 and add it to eq 2
x+3y+8z=22
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4x+14z=58 %%%%%%
Now we will work with equations i marked with %%%%%
3x+9z=27
4x+14z=58
So first one we'll multiply by -4 and second one by 3 and add them
-12x-36z=-108
12x+42z=174
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6z=66 divide each side by 6 and you get
z=11 Now lets plug that into the first equation that i maked with %%%%%
3x+9*11=27
3x+99=27
3x=-72
x=24
Now lets plug z and x into the third original equation marked 3) and solve for y (i picked this one because it has less coefficients, so less work for us)
x-y+2z=12
24-y+2*11=12
24-y+22=12
46-y=12
-y=-34
y=34
So the solution is (24,34,11)
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