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Question 331483: This site is for tutors to help not make the questions harder so nayone but john please help with this question. Solve the system x+y+z=-1
x-y+3z=-17
2x+y+z=-2
Found 2 solutions by mathmandotcom, Edwin McCravy:
Answer by mathmandotcom(31)   (Show Source):
You can put this solution on YOUR website! x+y+z=-1
x-y+3z=-17
2x+y+z=-2
adding the first two we eliminate y
2x+4z=-18
adding equations 2 and 3 we eliminate y
3x+4z=-19
now we have two equations and two unknowns
2x+4z=-18
3x+4z=-19 multiply (2x+4z=-18)*-1 and add
-2x-4z=18
3x+4z=-19 adding we eliminate z
x=-1 substitution 3(-1)+4z=-19
-3+4z=-19 add 3 to both sides
4z=-16 divide by 4
z=-4 substitution x=-1,z=-4 to the original
x+y+z=-1
-1+y-4=-1
-5+y=-1 add 5
y=4
(x,y,z)=(-1,4,-4) answer
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
1. Pick a letter to eliminate and two equations that contain it to
eliminate it from.
I will pick y to eliminate, and the first two equations to eliminate it
from:
Add corresponding terms and the y's drop out:
Since all the coefficients are equal, do let's divide every term by 2
2. Eliminate the same letter, y, from two equations that contain it to
eliminate it, but this time use the equation that you haven't used
yet
I will eliminate y from the second and third equations to eliminate it
from:
Add corresponding terms and the y's also drop out:
Now we have two equations in two unknowns
I will eliminate z by multiplying the first equation by -2:
Add them term by term and the z's drop out:
Substitute -1 for x in one of those equations, say
Now substitute -4 for z and -1 for x in one of the
original equations, say this one
So the solution is
(x,y,z) = (-1,4,-4}}}
Edwin
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