All categories

3 years ago

Solve the following system equations:

2 answers:

azamat3 years ago

7 0

(1).. 2x + 4y - 3z = -7
(2).. 3x + 1y + 4z = -12 
(3).. 1x + 3y + 4z = 4 

****************** 
ok.. we're going to put this into matrix form.. where we drop x, y, and z 
2.. 4.. -3.. | ... -7 
3.. 1.. .4.. | ... -12 
1.. 3.. .4 . | ... 4 
ok? 

now.. I'll designate the rows (1), (2), (3).. ok? 
new (1) = -2x(3) + (1) 
new (2) = -3x(3) + (2) 
ie... 
0..-2..-11. | .. -15 
0..-8.. -8.. | ... -24 
1.. 3.. .4 . | ... .+4 

new row (2) = old (2) / -8 
0..-2..-11. | .. -15 
0.. 1.. 1.. | ... +3 
1.. 3.. .4 . | ... +4 

new (1) = 2xold(2) + 1 
new (3) = -3xold(2) + 3 
0.. 0..-9 .. | ... -9 
0.. 1.. 1.. | ... +3 
1.. 0.. .1 . | ... -5 

new row(1) = old row 1 /-9 
0.. 0.. .1 .. | ... +1 
0.. 1.. 1.. | ... +3 
1.. 0.. .1 . | ... -5 

new (2) = old(2) - old(1) 
new (3) = old(3) - old(1) 
0.. 0.. .1 .. | ... +1 
0.. 1.. 0.. | ... +2 
1.. 0.. .0 . | ... -6 

so.. (x,y,z) = (-6, +2, +1)..

the last answer is correct

adell [148]3 years ago

3 0

Answer:

The solution is (–6, 2, 1). (Option A)

Step-by-step explanation:

Given three equations

2x + 4y - 3z = -7 → (1)

3x + y + 4z = -12 → (2)

x + 3y + 4z = 4 → (3)

we have to find the solution of above equations.

By elimination method

Multiply equation (2) by 4 and then subtracting from (1), we get

(2x + 4y - 3z+7)-4(3x + y + 4z + 12)=0

⇒ -10x-19z=41 → (4)

Multiply equation (2) by 3 and then subtracting from (3), we get

(x + 3y + 4z - 4)-3(3x + y + 4z + 12)=0

⇒ -8x-8z=40 ⇒ x+z=-5 → (5)

Solving (4) and (5), we get

-10x-19z-41+10(x+z+5)=0

⇒ -9z=-9 ⇒ z=1

⇒ x+1=-5 ⇒ x=-6

and (3) implies -6 + 3y + 4 = 4 ⇒ y=2

Hence, the solution of above 3 equations will be (x,y,z)=(-6,2,1)

Hence, option (1) is correct.

You might be interested in

I NEEED HELPPP PLZZZZZZZZZZ

Sonbull [250]

For the congruent statement LMNOP = HFSYA

8 0

3 years ago

Which is > < or =, 2/3 or 6/10

LuckyWell [14K]

2/3 is the bigger fraction

8 0

3 years ago

17. The distance between (2, 1) and (n, 4) is 5 units. Find all possible values of n.

Rufina [12.5K]

Answer:

6=n and -2=n

Step-by-step explanation:

The distance between two points is found by

d = sqrt(( x2-x1)^2 + (y2-y1)^2)

5 = sqrt(( n-2)^2 + (4-1)^2)

5 = sqrt(( n-2)^2 + (3)^2)

Square each side

5^2 = sqrt(( n-2)^2 + (3)^2)^2

25 = ( n-2)^2 + (3)^2

25 = (n-2)^2 +9

Subtract 9 from each side

25-9 = (n-2)^2 +9-9

16 = (n-2)^2

Take the square root of each side

sqrt(16) = sqrt( (n-2)^2)

±4 = n-2

Add 2 to each side

2±4 = n-2+2

2 ±4 = n

2+4 =n and 2-4 =n

6=n and -2=n

5 0

4 years ago

You are studying 112 returning combat veterans with deployment related injuries. You are testing a cognitive impairment screen t

svlad2 [7]

Answer:

0.9894 = 98.94% probability that he does not have a TBI.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Negative screen

Event B: Does not have a TBI.

Probability of a negative screen:

93 are negative and do not have a TBI.

1 is negative and has a TBI.

Out of 112.

$P(A) = \frac{93+1}{112} = \frac{94}{112}$

Probability of a negative screen and not having a TBI:

93 are negative and do not have a TBI, out of 112, so:

$P(A \cap B) = \frac{93}{112}$

One of the veterans has a negative screen and wants to know the probability that he does not have a TBI.

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{93}{112}}{\frac{94}{112}} = \frac{93}{94} = 0.9894$

0.9894 = 98.94% probability that he does not have a TBI.

6 0

3 years ago

What is the distance between the two points located at (9, 12) and (9, −11)?

Vilka [71]

Answer:

23 units

Step-by-step explanation:

Because the X value in each coordinate point is the same, we only need to subtract the the Y values to find the distance.

12 - (-11) = 23

3 0

3 years ago