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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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Answer:

(a)  |0 - 8| = 8

(b)  |-4 - 6| = 10

Step-by-step explanation:

Given

Attached number lines

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Solving (a):

Let:

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A power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water i
nlexa [21]

Answer:

(A) Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) Type II error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is no more than 150°F but in actual the mean temperature of the discharged water was more than 150°F.

(C) An environmental group will consider the Type II error more serious.

Step-by-step explanation:

We are given that a power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water is no more than 150°F, there will be no negative effects on the river’s ecosystem.

We are also given with the following hypothesis;

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Alternate Hypothesis, H_a : \mu > 150°F

(A) <u><em>Type I error</em></u><em> states that Probability of rejecting null hypothesis given the fact that null hypothesis was true or in other words Probability of rejecting a true hypothesis.</em>

So, Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) <u><em>Type II error </em></u><em>states that Probability of accepting null hypothesis given the fact that null hypothesis was false or in other words Probability of accepting a false hypothesis.</em>

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