How to solve systems of equations by substitution with 3 variables?

Answers

Answer 1

To solve the system of equations using substitution method for three variables minimum three equations are required using following steps:

1. Get the value third variable in form of other two and substitute in other two equations.

2. Now get the value of second variable in first variable and get the value of all three variables.

Let us consider three system of equations in three variable are :

x + y + z = 0   __(1)

2x + 3y + z = 2 __(2)

3x + 2y + 2z = 1  ____(3)

Get the value of z in form of x and y from (1) and substitute in (2) and (3)

z = -(x + y)

2x + 3y -(x + y) = 2

⇒x +2y = 2   __(4)

3x + 2y +2(-(x +y)) = 1

⇒3x + 2y -2x -2y =1

⇒x = 1

Now substitute in (4)

1 + 2y = 2

⇒ y = 1/2

Now substitute the value of x and y in (1)

z = - ( 1 + 1/2)

⇒z = -3/2

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Related Questions

find the area of the shape​

Answers

Answer:

Step-by-step explanation:

Answer:

=> 1/4  * [tex]\pi r^{2}[/tex]

=> 1/4 * 3.14 * 4

=> 3.14

Answer = 3.14

Please mark my answer as the brainliest for further answers :)

75250 tickets were available for an international cricket match. 62% of the tickets were sold
within a day. How many tickets are left?​

Answers

Answer:

46655

Step-by-step explanation:

[tex]75250 \cdot \frac{62}{100} = 46655[/tex]

A) If 4 farmers can plow a 3-hectare land in 6 days, how long will 8
farmers do it?​

Answers

Answer:

I believe that It will take 3 days if 8 farmers will plow 3-hectare land.

Step-by-step explanation:

The work doubled so days will be less in a half.

I guess if 4 can finish it in 3 days then 8 will finish in half the time they took so I think they will finish in a day and a half

Can somebody please help me with multiplying fractions and it would be really helpful to show examples

Answers

Try looking up the butterfly method! You basically multiply denominator with the numerator for both sides - I can’t explain too well but I think a video would be best to understand

Step-by-step explanation:

hey, hope this helps. :)

15 POINTS!

1. You throw a ball through a hoop once 8 tries. How many balls can you predict you will throw the hoop 56 tries?


2. You Flip A fair coin 16 times. How many times can you expect the coin to come up tails?


3. You Hit A Ball 90% of the time. Predict how many times you will hit the ball in 200 times

Do The One that you want

Answers

Answer:

Step-by-step explanation:

1. 56/8= 7 = Amount of tries

2. 16/2= 8 = Coin to come up tails  (It's a 50/50)

3. I'll skip this one.

1. 7 because 56/8=7
2. 8 because 16/2=7
3. 180 because 90/100= x/200 so you multiply 200x90 then divide by 100

What is the area of the base ? / / / / /

Answers

Answer:

area of base = 20 in²

Step-by-step explanation:

area of base = 2 x 10 = 20 in²

Find the missing length of the right triangle.

Answers

20, because by using Pythagorean theorem, a2+b2=c2. Let’s make a=12 and b=16. (12)2 + (16)2 =c2. If you simplify this, 144 + 256 = c2. 144 + 256 = 400, so 400=c2. Finally if we take the square root of both sides, c=20.

Based on the scatter plot, what type of association is shown between hours of sleep and test scores?

A: Positive Association

B: Negative Association

C: No Association

Answers

This is easily (A) Positive Association

PLEASE HELP ME I WILL MARK BRAINLIEST (ITS DUE IN A HOUR)

Answers

Answer:

the equation is 9.75c=20.75

then the amount is 2.13

Step-by-step explanation:

Answer: c - 9.75 = 20.75

  flip it   20.75 - 9.75 = c

             -  9.75

        ____________

                11.00

C = 11.00

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Answers

Answer:

1st one is a function, 2nd is a funtion, 3rd is a function, 4th is not a function, 5th is not a function, 6 is a function

Step-by-step explanation:

Hope it helps :) You can see if a graph is a function by performing the vertical line test.

Find the surface area

Answers

Answer:

100

Step-by-step explanation:

i think

It is the cubicle shape

Therefore, 6l² is the formula to find surface area of cube

Area of cube = 6(10)²

Therefore, 6*100

Therefore, 600

Area of cube =600ft²

what is the combined length of 5/8

Answers

5/8 + 5/8 + 5/8 = 15/8 = 1 7/8 inches.

what is the median and mode for the numbers 40, 28, 24, 37, 43, 26, 30, 36

Answers

Answer:

Median

Assending order =24,26,28,30,36,37,40,43

It is even no of obs

Therefore the two middle obs are 30,36

Therefore median 30+36/2

Therefore median 66/2

Therefore median is 33

There is no mode in the following obs

If you are helped with my answer pls tag me brianliest I really want it

THANK YOU.......

The median of the numbers is M = 33 and the mode is not defined

What is Median?

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

Let the set of numbers be represented as set A

Now , the value of A is

A = { 40, 28, 24, 37, 43, 26, 30, 36 }

Arranging the numbers in the ascending order , we get

A = { 24 , 26 , 28 , 30 , 36 , 37 , 40 , 43 }

Now , the total number of elements in the set A = 8

So , the median is the average of the two middle data points in the list.

M = ( 30 + 36 ) / 2

M = 33

The mode of the numbers is the numbers that appears the most often

So , mode is not defined

Hence , the median is M = 33

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help plz look at the image to answer to all 10 questions no links plz

Answers

Answer:

2 4 6 8 12 14 16 18 20

Step-by-step explanation:

Answer:2 4 6 8 10 12 14 16 18 20

Step-by-step explanation: just add them or count by 2

I need help with some scientific notation problems

Answers

Answer:

1) 4.5 x 10^3 =4,500

2)5.78 x 10^-2

3) 5.7 x 10^1 = 57

4) 6.256 x 10^-3 = 0.006256

5) 7.3 x 10^2 = 730

6) 4.2 x 10^-5 = 0.000042

7) 7x10^-3 = 0.007

8) 2.563 x 10^1

9) 3.0025 x 10^2 = 300.25

10) 1.456 x 10^-1

find the inverse of h(x)= -x^5+2 step by step

Answers

Hi there!

[tex]\large\boxed{y = \sqrt[5]{-(x-2)}}[/tex]

[tex]h(x) = -x^{5} + 2[/tex]

Rewrite h(x) as y:

[tex]y = -x^5 + 2[/tex]

Switch the x and y variables:

[tex]x = -y^{5} + 2[/tex]

Isolate y by subtracting 2 from both sides:

[tex]x - 2 = -y^5[/tex]

Multiply both sides by -1:

[tex]-(x-2) = y^5[/tex]

Take the 5th root of both sides:

[tex]y = \sqrt[5]{-(x-2)}[/tex]

Classify the polynomial by degree and number of terms.
-2x² + x4 +3
constant
linear
quadratic
cubic
quartic
monomial
binomial
trinomial

Answers

Answer:

linear

Step-by-step explanation:

Answer: its a trinomial

Step-by-step explanation:

What does the constant term in the above expression represent? A. The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold. B. The constant -10 represents the maximum number of cheeseburgers sold by the food stall at the funfair. C. The constant -10 represents the total money earned by setting up the food stall. D. The constant -10 represents the cost of each cheeseburger at the food stall.

Answers

Answer:

In the expression [tex]\dfrac{60 \cdot x}{x + 3} -10[/tex] what the constant term -10 represents is;

A. The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold

Step-by-step explanation:

Whereby the expression is as given in a similar question which is presented as follows;

[tex]\dfrac{60 \cdot x}{x + 3} -10[/tex]

Where the expression represents the total money earned when a food stall is set up at a fair where 'x' stands for the number of cheeseburgers sold

Then when no cheeseburger were sold, x = 0, such at the start just after setting up the food stall,  we then have;

[tex]\dfrac{60 \times 0}{0 + 3} -10 = -10[/tex]

Therefore, the money earned at the start = -10

∴ The money spent at the start = 10

Therefore, the constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.

When looking for a job micah is told that the monthly salary has a range of 876 he also knows that the starting salary is 1,793 per month what is the maximum amount of money that micah can earn in this position?

Answers

Answer:

2669

Step-by-step explanation:

Given that :

Salary range = 876

Starting salary = 1793 monthly

The starting salary represents the minimum amount Micah can earn monthly

Therefore, the amount of money much can earn can be calculated thus :

Recall :

Range = maximum - minimum

876 = maximum - 1793

876 + 1793 = maximum

Maximum = 2669

Hence, the maximum salary Micha can earn is 2669 monthly

An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below. Weight (pounds), x Miles per Gallon, y 3773 17 3793 16 2706 25 3645 20 3308 22 2908 24 3675 17 2687 24 3522 18 3827 16 a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable y= x+( ) A certain​ gas-powered car weighs 3511 pounds and gets 18 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight? ​The estimated average miles per gallon for cars of this weight is ( ) miles per gallon. The miles per gallon of this car is average for cars of this weight.

Answers

Answer:

y= 0.007x- 4.945

The estimated average miles per gallon for cars of this weight is (20.829 or 21 ) miles per gallon.

The miles per gallon of this car below (18 < 20.829) the average for cars of this weight.

Step-by-step explanation:

Weight                   Miles              

(pounds), x    per Gallon,   y             xy

3773                       17                     64,141

3793                       16                     60,688    

2706                      25                    67,650

3645                       20                  72,900

3308                         22                 72,776

2908                        24                   69,792

3675                         17                    62,745  

2687                        24                   64,488

3522                        18                     63,396

3827                        16                      61,232

∑y²=4075; ∑y=199;    ∑x²= 116,406,174 ; ∑x=33,844 ;  ∑xy=659,808

b= n∑XY - (∑X)(∑Y)/ n∑X² - (∑X)²

b=(10) (659,808) - (33,844)(199)/ 10 (116,406,174) - 1,145,416,336

b=6,598,080- 6,734,956/ 1,164,061,740 -1,145,416,336

b=136,876/18,645,404

b= 0.007341

a= Y`- bX`

a= 19.9- (0.007341) (3384.4)

a= 19.9 -24.845

a=-4.945

Y^= -4.945+ ( 0.007341) X

y= 0.007x- 4.945

Putting the values

y= 0.007x- 4.945

18 = 0.007(3511) - 4.945

18< 20.829

​The estimated average miles per gallon for cars of this weight is (20.829 or 21 ) miles per gallon.

The miles per gallon of this car below (18 < 20.829) the average for cars of this weight.

WHAT IS A EQUATION PLEASE HELP!

Answers

Answer: 1.5s+20

Step-by-step explanation:

omg I need help w all the questions lol someone pls help me. If u can message me and tell me or help me w the answers

Answers

What’s the height?
Formula is: V= πr2h
d=4 in
r=2 in
V= π•2^2•h
V= π•4•h
If h is 3, answer is B. If h is 9, answer is C. Good luck.

6. Find the quotients.
a. 0.024 : 0.015
b. 0.24 : 0.015
c. 0.024 : 0.15
d. 24 = 15

Answers

Answer:

please provide an image or the equation! would love to help.

Step-by-step explanation:

Workers mixed 7 gallons of blue paint, 4 gallons of yellow paint, and 1 gallon of white paint to make a special shade of paint . They will use a total of 108 gallons of this mixture to paint the offices in a building .Based on this information, complete the following statements.

They will use _______times as much yellow paint as white paint.

They will use a total of _______gallons of blue and yellow paint.

They will use _________more gallons of blue paint than of white paint.

Answers

Answer:

What’s the answer

Step-by-step explanation:

A cell phone company charges a one-time activation fee, as well as a monthly service charge for a cell phone plan with unlimited minutes and data. The total cost is modeled by the function C(x) = 99 + 85x. Which statement represents the meaning of the function?

Answers

Answer:

C(x) is the total cost, x is the number of months of service, $99 is the one-time activation fee, and $85 is the service charge per month.

Step-by-step explanation:

Because I'm always right.

PLEASE HELP !!!!!!!!
What is the arc measure of arc PQO? Type the answer as a number only.

Answers

Answer: !50 is the answer hope this helped

Step-by-step explanation:

Which of the following is equivalent to the expression below?

Answers

Answer:

C is the answer

Step-by-step explanation:

What is this equation -4(y-2)=12

Answers

Answer: -1

Explanation:

-4(y-2)=12
y-2=-3
y=-1

I need help!! Bill will spend at most $29 on gifts. So far, he has spent $13. What are the possible additional amounts he will spend? 

Answers

Answer:

$ is less than or equal to $16

Step-by-step explanation:

The area of a square is a function of the length of the side of the square.

Answers

Answer: A =a2

Step-by-step explanation:

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Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of an answer to a question is independent of the correctness of answers to other questions. Jodi is a good student for whom p = 0.81.Required:a. Use the Normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test.b. If the test contains 250 questions, what is the probability that Jodi will score 77% or lower?c. How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also? You are sailing your boat in the Chesapeake Bay to Thomas Point Lighthouse. You see a weather buoy, and you discover that your boat, the buoy, and ThomasPoint form a right angle using your navigational skills.What is the value of x? - 20 km - 8 km - 12 km- 17.3 km A square has an area of 200 square feet. How long is each side in simplest radical form? If I increase the length of each side by 2, what is the new area in simplest radical form? HELP ASAP I WILL MARK BRAINLIEST PLS NO LINK I DONT WANT TO DO BAD ON THIS ASSIGMENT The International Space Station (ISS) orbits Earth 254 miles above. It takes about 48 hours to get from Earth to the ISS. What is the average speed of the spacecraft? Round to the nearest hundredth (two decimal places). Speed = why don't we ever see solid or liquid oxygen on earth? List 3 political reasons for the Vietnam War. 2 negative aspects of the Vietnam War. Explain the significance of 1 individual from the Vietnam War. Find the perimeter of a triangle with side lengths of 3x, x + 2, and x 4. what property is used here 3(+2)=3+6 Write the steps for calculating molar mass. Why is the air you breathe more likely to enter the right lung than the left? How can we use science and math to develop a cost-benefitanalysis to help manage natural resources? Which Texan piloted the first manned flight in the Apollo mission?Select one: Michael DeBakey Edward H. White Walter Cunningham Benjy Frances Brooks Given a function f(x)=|x+1|-|x -2|How many solutions has f(x) = a, in respect of a?If a E {-3, 3}, number of solutions isif a E (-3, 3) number of solutions isif a E (-infinity, -3) U (3,infinity) number of solutions is The force of Earths gravity keeps earth in orbit true or false 7. Jerry has 23 coins in nickels, n, and dimes, d. Hehas $1.95 altogether. How many nickels does Jerryhave? Read the excerpt from "The Lottery."The children assembled first, of course. School was recently over for the summer, and the feeling of liberty sat uneasily on most of them; they tended to gather together quietly for a while before they broke into boisterous play, and their talk was still of the classroom and the teacher, of books and reprimands.What information from the excerpt is ironic?The children are still thinking about school now that is summer.The children gathered quietly together.The children arrived first for the lottery.The feeling of freedom from school is an uneasy one. Pls help if you can Thx! lve had a crush on a girl for 4 years now,Do i love her or its still just a crush 18. Paris tends to view personality as fairly stable and therefore her personality is more stable, whereas Lanetends to view personality as fairly changeable and therefore her personality is more changeable. Thesedifferences in attitudes and personality are most consistent with theneed help asap Can someone tell me if this is correct