Use the method of elimination to determine whether the given linear system is consistent or inconsistent. If it is consistent, find the solution if it is unique, otherwise describe the infinite solution set in terms of an arbitrary parameter t. (Note that a system of equations is said to be consistent if it has at least one solution)

4x - 2y + 6z = 0
-y-z=0
- y + 3z = 0

Answers

Answer 1

Answer:

Step-by-step explanation:

From the given information;

We will realize that in the 2nd & 3rd equation, the integer "x" is missing.

So, the correct equation should be:

4x - 2 + 6z = 0

x - y - z = 0

2x - y + 3z = 0

By rearrangement; if we switch equation (1) and (2)

x - y - z = 0      ----- (1)

4x - 2 + 6z = 0 ------ (2)

2x - y + 3z = 0  ------ (3)

If we multiply equation (1) and add that to  equation (2);

Then, we have:

x - y - z = 0

2y + 10z = 0

2x - y + 3z = 0

Also, if we multiply equation (1) by -2 and add that to equation (3), we have:

x - y - z = 0

2y + 10z = 0

y + 5z = 0

From above recent equation, if we swap equation (2) and (3);

x - y - z = 0

y + 5z = 0

2y + 10z = 0

Then, multiply equation (2) with -2, followed by adding it to equation(3);

Then:

x - y - z = 0

y + 5z = 0

0 = 0

Now, there exists no equation (3). Thus, let assume z = t to solve for x & y

y + 5z = 0

y = -5t

Similarly;

x - y - z = 0

x = -5t + t

x = -4t

Hence;

x = -4t; y = -5t; &  z = t


Related Questions

What is
1. (1-1/4) x 4
2. 2- 1/4 x4 +4
3. 8 + 10 x 1/2

Answers

Answer:

1. 3

2. 5

3. 13

Step-by-step explanation:

there is your answers :)

Elijah's uncle gave him $300 to spend on baseball equipment. He bought a pair of cleats for $69.99, two baseball jerseys for $32.99 each, a new glove for
$79.99 and two pair of socks for $6.99 each. Without including tax, to the nearest dollar, how much money did Elijah have left?

Answers

9514 1404 393

Answer:

  $70

Step-by-step explanation:

The amount Elijah has remaining is ...

  $300 -(70 +2×33 +80 +2×7) = $300 -(70 +80 +2(33 +7)) = $300 -230 = $70

To the nearest dollar, Elijah has $70 left.

_____

Each amount is within a penny of the nearest dollar, so we can simply use the nearest dollar amounts for the prices. In order for the answer to be different, Elijah would have to purchase 50 or more items with this pricing (something.99).

Mary is having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

A) If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.
B) Splash of Color will always charge the least.
C) If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.
D) If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.
E) If it takes 3 hours to paint the rooms, both companies will charge the same amount.

Answers

Answer:

A and E

Step-by-step explanation:

A) 7 hrs in IDU will cost you $305.00 while SC cost $385

B) 4hrs in and SC will charge you more than IDU by $20

C) SC charges you more than IDU by $50 so IDU is more cost effective

D)SC will charge you $140 more than IDU but not $200

E) 55 x 3 = 165 while 35 × 3 105 plus 60 is 165 therefore it is the same

x
What are the perimeter and area
of a square with side length of 12 in.?
A. P= 24 in., A = 24 in.?
B. P= 144 in., A = 48 in.2
O
C. P = 24 in., A = 144 in.2
O
D. P= 48 in., A = 144 in.2

Answers

Answer: P = 48 in, A = 144 in.2

Step-by-step explanation: Since a square has equal sides and we know one side length is 12 inches, then all the sides are 12 inches. For perimeter, we add all sides, which would equal 48 and for area, we multiply 2 of the sides, which would be 144.

Traci has 8 yards of fabric. She uses 10 feet of this fabric to make pillows. How much fabric does Traci have left

Answers

Answer:

She has 14 feet left

Step-by-step explanation:

1 yard = 3 feet of fabric

8 yards x 3 feet/yard = 24 feet

24 - 10 = 14 feet

HELPPP!!! i need to know this asap!!

Answers

Answer:

The first option

(-10, -7)

Step-by-step explanation:

Also I really like your pfp <33

Help please!!
Brainliest if right

Answers

Answer:

top and bottom

Step-by-step explanation:

Frank has 6 red socks, 8 black socks, and 10 white socks in his sock drawer. If Frank blindly reaches into his sock drawer, what is the probability that he will select a white sock and then another white sock? Round to the nearest percent A. 9% B. 16% C. 41% D. 80%​

Answers

Answer:

B

Step-by-step explanation:

The first probability is 10/24, and the second is 9/23. If you multiply these two fractoins you get 15/92. 15/92 is approximately equal to 16%.

What is the solution to this equation?
In(2x + 4) = ln(x + 3)

Answers

x= -1 !! hope this helps

The solution to this equation, [tex]ln(2x + 4) = ln(x + 3)[/tex] is  [tex]x=(-1)[/tex] .

What is log ?

A logarithm is the power to which a number must be raised in order to get some other number .

We have,

[tex]ln(2x + 4) = ln(x + 3)[/tex]

Now, apply log rules

As we have [tex](ln)[/tex] on both which will be cancel out,

    [tex]2x+4=x+3[/tex]

    [tex]3x=3-4[/tex]

    [tex]x=(-1)[/tex]

So, on getting solution to the given equation we get the value of [tex]x=(-1)[/tex] .

Hence, we can say that the solution to this equation, [tex]ln(2x + 4) = ln(x + 3)[/tex]  is  [tex]x=(-1)[/tex] .

To know more about log click here

https://brainly.com/question/82295

#SPJ2

If X = 12 inches, Y = 16 inches, and Z = 20 inches, what is the tangent of

Answers

Answer:

who do pow en odd an odd an 9 all 9 FM

recipe calls for 1/3 of a cup of milk for 10 cookies how many cups of milk are needed to make 90 cookies

Answers

Answer:

just multiply by 9 :)

Step-by-step explanation:

Solve 4r2 – 5 = 59
{± 3}


{± 4}


{± 5}


{±6}

Answers

9514 1404 393

Answer:

  (b)  ±4

Step-by-step explanation:

  4r^2 -5 = 59 . . . . given

  4r^2 = 64 . . . . . . . add 5

  r^2 = 16 . . . . . . . . . divide by 4

  r = ±4 . . . . . . . . . . . take the square root

Find the common difference of the arithmetic sequence -2, -4, -6, ...

Answers

Answer:

-8

in this the arthmatic difference is table of 2

Answer:

the common d/f is that -2>-4>-6

You invest $17,804 in a CD that has a 6.275% annual interest rate, compounded continuously. How much will you have in 25 years?Round to the nearest cent.

Answers

Answer:

R = 3.813% per year.

Step-by-step explanation:

A = Accrued amount (principal + interest) P = Principal amount r = Annual nominal interest rate as a decimal R = Annual nominal interest rate as a percent r = R/100 n = number of compounding periods per unit of time t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years. I = Interest amount ln = natural logarithm.

please help me someone i really need this to get my grade up :(

Answers

Answer: D

2 1/2 divided by 1/4 = 10

hope this gets ur grade up keep trying ur best!! :D

the sum of 8 and joses score is 35 use the variable j yo represent josés score​

Answers

Answer:

8 + j = 35

subtract 8 from both sides

j = 27

Step-by-step explanation:

VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.

Answers

Answer:

(2, 5)

Step-by-step explanation:

(x,y) -> )- y,x)

Determine the margin of error for a 90% confidence interval to estimate the population mean when s = 40 for the sample sizes below.
a) n=14
b) n = 28
c) n = 45
a) The margin of error for a 90% confidence interval when n = 14 is
(Round to two decimal places as needed.)
b) The margin of error for a 90% confidence interval when n=28 is
(Round to two decimal places as needed.)
c) The margin of error for a 90% confidence interval when n = 45 is
(Round to two decimal places as needed.)

Answers

Answer:

a) The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is 10.02.

Step-by-step explanation:

The t-distribution is used to solve this question:

a) n = 14

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7709

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) n = 28

27 df, T = 1.7033

[tex]M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88[/tex]

The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is

44 df, T = 1.6802

[tex]M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02[/tex]

The margin of error for a 90% confidence interval when n = 45 is 10.02.

question is in picture please help!

Answers

Answer:

I’m not 100% sure but I think 120°.

Step-by-step explanation:

This is because, angles on a straight line add up to 180°. Because there is 60 degrees on one side of line B, this means the other section is 120° (120°+60°=180°) The angle labelled (3x) is alternate to the angle of 120°. Alternate angles are always equal, meaning that 3x is equal to 120°.

I hope this is right.

I don’t understand this...I’ve tried reading for answers, but this question stumps me. Please help!

Answers

Answer:

x=1, y=-5

Step-by-step explanation:

4(1)+2y=-6

2y=-10

y=-5

or

-3x-2(-5)=7

-3x=-3

x=1

Hope this helps!

Answer: x=1 y=-5

Why? I did the math for you! Start in the top left corner and follow the arrows

Solve. Write or draw to explain. Amy has 12 stickers. Jen has 9 stickers. They place 7 stickers on each page of a book. How many pages are in the book? Math Spot thpicks​

Answers

Answer:

There's 3 pages in the book

Step-by-step explanation:

You add both of the amounts of stickers (12+9=21), then you divide by the amount on each page (21÷7=3)

Hope this helped!

7. Mrs. Paulson is constructing a 90% confidence interval for the difference of means based on independent
simple random samples from two populations. The sample sizes are n, = 6 and n, =14. She draws dotplots
of the sample data to check one of the conditions for using two-sample i procedures. Which of the following
descriptions of those dotplots would suggest that it is safe to perform inference?
(a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.
(b) Both dotplots are roughly symmetric. The dotplot of sample 2 has an outlier.
(c) Both dotplots are strongly skewed to the right. There are no outliers in either dotplot.
(d) Both dotplots are roughly symmetric. Both dotplots have one upper outlier
(e) i procedures are not recommended in any of these cases.

Answers

The description that will show that it is safe to perform inference is that (a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.

What description would make it possible to make inferences?

In order to use the two-sample t procedure to make inferences, certain conditions need to be met such as the sample being random and independent.

The variances for the groups in the data need to be equal which is why the presence of no outliers in either dotplot would present an safe opportunity to be able to perform inferences on the data.

In conclusion, option A is correct.

Find out more on two-sample t-tests at https://brainly.com/question/17438355.

Can someone help me with these two questions

Answers

the answer your looking for is C.

Please help ASP!!!! A= positive, B=Negative, C=Zero​

Answers

Answer:

B. Negative

Step-by-step explanation:

So first, we want to locate the variable.

y (x/y) = (y/1) (x/y)

           = (xy/y)

           = x

The y/y cancels out and now we know we need to find the sign of x. Because x is to the left of 0, it's negative. Anything to the left decreases and anything to the left of 0 is (-).

Jessica is making a cake. The recipe calls for 2 3/4 cups of flour. She only has a measuring cup that holds 1/4 cup. Explain how she can use the measuring cup that holds 1/4 cup to measure 2 3/4 cups of flour.

Answers

Answer: Jessica can use her measuring cup 11 times.

(hope this helps!)

Help- this is also due tomorrow-

Answers

45???? dont u just subtract 180 by that then get the missing angle?

Answer:

46

Step-by-step explanation:

200 miles divided by 8​

Answers

Answer:

25

200 divided by 8 is 25.

Step-by-step explanation:


Find dy/dx
for 4 tan^2x - xy^2= sin2y by using implicit differentiation

Answers

Answer:

Y=bx+c

Step-by-step explanation:

That should be right

Answer:

Y=bx+c

Step-by-step explanation:

Please help please help please help

Answers

It should be 986m

4(17x6)= 408
2(17x17)= 578

408+578=986

help me plz.................

Answers

Answer:

[tex]\frac{1}{8}[/tex] cup

Step-by-step explanation:

[tex]y=\frac{7}{8} -\frac{1}{4}-\frac{1}{2}[/tex]

[tex]y=\frac{7}{8}-\frac{2}{8}-\frac{4}{8}[/tex]

[tex]y=\frac{7}{8}-\frac{6}{8}[/tex]

[tex]y=\frac{1}{8}[/tex]

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