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kaheart [24]
3 years ago
8

How would you go about finding the solution to this system of three equations in three variables? Be specific. For example, you

might want to add the first two equations first, or multiply the third one by two first and use elimination, etc. (No right answer exists.)
2x – y + z = 7

x + 2y – 5z = -1

x – y = 6
Mathematics
1 answer:
kupik [55]3 years ago
3 0
I:2x – y + z = 7
II:x + 2y – 5z = -1
III:x – y = 6

you can first use III and substitute x or y to eliminate it in I and II (in this case x):
III: x=6+y
-> substitute x in I and II:
I': 2*(6+y)-y+z=7
12+2y-y+z=7
y+z=-5

II':(6+y)+2y-5z=-1
3y+6-5z=-1
3y-5z=-7

then you can subtract II' from 3*I' to eliminate y:
3*I'=3y+3z=-15

3*I'-II':
3y+3z-(3y-5z)=-15-(-7)
8z=-8
z=-1

insert z in II' to calculate y:
3y-5z=-7
3y+5=-7
3y=-12
y=-4

insert y into III to calculate x:
x-(-4)=6
x+4=6
x=2

so the solution is
x=2
y=-4
z=-1
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