What is the solution to the system of equations?
x-y+2z=9
3x+y=z=2
2x-y+z=8

Answers

Answer 1

Answer:

x=8/7, y=-25/7, z=15/7

Step-by-step explanation:

x-y+2z=9 ==> equation 1

3x+y=z=2 ==> equation 2

2x-y+z=8 ==> equation 3

  3x+y+z=2

+ (2x-y+z=8)

3x+2x + y+(-y)  + z+z = 2+8  ==> add equation 2 and 3 to eliminate y

 5x + 2z = 10  ==> equation 4

  x-y+2z=9

- (2x-y+z=8)

x - 2x + (-y)-(-y) + 2z-z = 9-8 ==> subtract equation 1 and 3 to eliminate y

-x + 0 + z = 1  ==> Let's say -y=a. (-y)-(-y) = a-a = 0.

(-x + z = 1)*2 ==> multiply by 2 to get z to become 2z

-2x + 2z = 2  ==> equation 5

   5x + 2z = 10

- (-2x + 2z = 2)

5x-(-2x) + 2z-2z = 10-2 ==> subtract equation 4 and 5 to solve for x

5x+2x = 8

7x = 8  ==> divide both sides by 7 to isolate x

x = 8/7

-2(8/7) + 2z = 2  ==> plugin x into equation 5 to solve for z

-16/7 + 2z = 2 ==> simplify

(-16/7 + 2z = 2)*7  ==> multiply the equation by 7 to eliminate fractions

-16 + 14z = 14

14z = 30  ==> add 16 on both sides to isolate z

z = 30/14  ==> divide each side by 14

z = 15/7  ==> simplify

2(8/7)-y+(15/7)=8  ==> plugin x = 8/7 and z = 15/7 into equation 3

16/7 - y + 15/7 = 8

(16/7 + 15/7 - y = 8)*7  ==> multiply the equation by 7 to remove fractions

16 + 15 - 7y = 56

31 - 7y = 56

-7y = 25  ==> subtract 31 on both sides to isolate y

7y = -25

y = -25/7

Answer: (x=8/7, y=15/7, z=-25/7)


Related Questions

What is the distance between (4, 3) and (7, 3)?

Answers

Answer:

3 units

Step-by-step explanation:

A rectangular banner covers an area of 2 7/8ft2. The length of the banner is 3/4ft. What is the width of the banner in ft?

Answers

Answer:

Width of the rectangular banner is [tex]3\frac{5}{6}[/tex] ft.

Step-by-step explanation:

Area of the rectangular banner = [tex]2\frac{7}{8}[/tex] square feet

                                                    = [tex]\frac{23}{8}[/tex] square feet

Area of rectangle is given by,

Area = Length × Width

Length of the banner = [tex]\frac{3}{4}[/tex] feet

From the formula,

[tex]\frac{23}{8}=\frac{3}{4}\times W[/tex]

W = [tex]\frac{\frac{23}{8} }{\frac{3}{4} }[/tex]

    = [tex]\frac{23}{8}\times \frac{4}{3}[/tex]

    = [tex]\frac{23}{6}[/tex]

     = [tex]3\frac{5}{6}[/tex] ft

Therefore, width of the rectangular banner is [tex]3\frac{5}{6}[/tex] ft

Use the greatest common factor and the distributive property to write equivalent expressions in factored form.

13ab + 15ab =​

Answers

Answer:

ab(28) or 28ab

Step-by-step explanation:

13ab + 15ab = 28ab

Answer:

ab(28) or 28ab

Step-by-step explanation:

mandy buys 36 pens, 36 pencils, 36 rulers and 36 pencil cases
what is the total amount of money spent by mandy

Answers

Answer:

Depends on how much each item cost but in this case if everything was a dollar it would cost $144.

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Find the slope of the linear equation 2y = -18x + 10

Answers

Go follow me on twitch and o got I

Answer:

m= -9

Step-by-step explanation:

Hope this helps

I need you to solve this for me and I need the steps and answer
+1x=+50

Answers

Answer:

x=50

Step-by-step explanation:

+1x=50

divide both sides by 1

x=50

Answer:

x = 50

Step-by-step explanation:

If you divide anything by one, it will remain the same.

To isolate the x variable, you need to divide both sides by 1.

+1x/1 = 50/1

x = 50

Diana decided she needed some new friends to play with. She understood that fish were not fun to hang out with, so she bought 3 baby mice and 2 baby pythons for a total cost of $103.50. Mr. Reyes also thought this was a great idea. He bought 3 baby mice and 3 baby pythons for a price of $148.50. Find the price of the mouse and the price of the python.

Answers

Step-by-step explanation:

Let m be the price of 1 baby mice

Let p be the price of 1 baby python

Given,

[tex]3m + 2p = 103.50[/tex]

as equation 1.

and

[tex]3m + 3p = 148.50[/tex]

as equation 2

From here we can easily use elimination method

for solving simultaneous equations.

Use Equation 1 - equation 2 to eliminate m to find p.

[tex](3m - 3m) + (2p - 3p) = 103.50 - 148.50 \\ - p = - 45 \\ p = 45[/tex]

Substitute p into equation 1.

[tex]3m + 2(45) = 103.50 \\ 3m + 90 = 103.50 \\ 3m = 103.50 - 90 \\ 3m = 13.50 \\ m = 13.50 \div 3 \\ = 4.50[/tex]

therefore 1 baby mice cost $4.50 and 1 baby python costs $45.

Answer:

Baby python: $45

Baby mouse: $4.5

Step-by-step explanation:

First of all, 3 baby mice and 2 baby pythons cost $103.50. When Mr. Reyes adds a baby python (He bought 3 baby mice and 3 baby pythons for a price of $148.50.) To find the price of a baby snake, you need to subtract both prices. 148.5-103.5=45, so a baby snake costs $45. Now we need to find the price of the baby mice, so we need to remove the snakes. 45*2=90. (2 snakes). 103.5-90=13.5, and 13.5/3=4.5, so a baby mouse costs $4.5.

Thanks

Solve the variable in the following equation: 5 + h = 11 − 2h
A. h = −1

B. h = 2

C. h = 5

D. h = 9

Answers

Answer: B. h = 2

Step-by-step explanation:

Given

5 + h = 11 - 2h

Add 2h on both sides

5 + h + 2h = 11 - 2h + 2h

5 + 3h = 11

Subtract 5 on both sides

5 + 3h - 5 = 11 - 5

3h = 6

Divide both sides by 3

3h / 3 = 6 / 3

h = 2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B) h=2

Step-by-step explanation:

5+h=11-2h

5+h-(-2h)=11

5+h+2h=11

5+3h=11

3h=11-5

3h=6

h=6/3

h=2

find the slope between the given two points​

Answers

Slope can be found using the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

7) Let:

[tex](x_1 , y_1) = (-1 , -11)\\(x_2 , y_2) = (-6 , -7)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{-7 - (-11)}{-6 - (-1)} = \frac{-7 + 11}{-6 + 1} = \frac{4}{-5} = -\frac{4}{5}[/tex]

Slope: [tex]-\frac{4}{5}[/tex]

8) Let:

[tex](x_1 , y_1) = (-7 , -13)\\(x_2 , y_2) = (1 , -5)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{-5 - (-13)}{1 - (-7)} = \frac{-5 + 13}{1 + 7} = \frac{8}{8} = 1[/tex]

Slope: [tex]1[/tex]

9) Let:

[tex](x_1 , y_1) = (-5 , 3)\\(x_2 , y_2) = (8 , 3)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{3 - (3)}{8 - (-5)} = \frac{0}{8 + 5} = \frac{0}{13} = 0[/tex]

Slope: [tex]0[/tex]

10) Let:

[tex](x_1 , y_1) = (3 , -2)\\(x_2 , y_2) = (15 , 7)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{7 - (-2)}{15 - 3} = \frac{7 + 2}{15 - 3} = \frac{9}{12}[/tex]

Simplify the slope. Divide common factors from both the numerator and denominator:

[tex](\frac{9}{12})/(\frac{3}{3} ) = \frac{3}{4}[/tex]

Slope: [tex]\frac{3}{4}[/tex]

11) Let:

[tex](x_1 , y_1) = (-5 , -10)\\(x_2 , y_2) = (-5 , -1)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{-1 - (-10)}{-5 - (-5)} = \frac{-1 + 10}{-5 + 5} = \frac{9}{0} =[/tex] undefined.

Slope: undefined

12) Let:

[tex](x_1 , y_1) = (-4 , -2)\\(x_2 , y_2) = (-12, 16)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{16 - (-2)}{-12 - (-4)} = \frac{16 + 2}{-12 + 4} = \frac{18}{-8} = -\frac{18}{8} = ((-\frac{18}{8})/( \frac{2}{2}) = -\frac{9}{4}[/tex]

Slope: [tex]-\frac{9}{4}[/tex]

~

Given m||n, find the value of x.

Answers

Answer:

The answer would be X=2 .

Step-by-step explanation:

Hope it helps u :)

GIVING BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 30pts-

Answers

Answer:

d

Step-by-step explanation:

How do u make 25 m to *what* cm?

Answers

Answer:

2500 cm

Step-by-step explanation:

1 meter = 100 cm

25m x 100 = 2500 cm

Answer:

25cm is equal to 2500 cm because 1 m is 100 cm

Step-by-step explanation:

Please, may i have brainly? i need 4 more!

Story is The Crystal Ball Brainliest for correct answers

Answers

Answer:

C.

Step-by-step explanation:

Though the story is also about A, B, and D, the overall story is about C. The story begins with the enchanter turning the eldest and second eldest brothers into an Eagle and Whale, though the youngest escapes. He then goes to the castle to free the cursed princess, and to do so he needs to find a crystal ball. If I remember correctly, the ball will also save the brothers.

ITS C

for the iready question it is C youngest brother tryna find the balls, i got it right

What is the slant height of a square pyramid that has a surface area of 319 square feet and a side length of 11 feet?

9 ft
10 ft
11 ft
8 ft

Answers

Answer:

the 319 square feet and side length of 11 feet is 10ft

ASAP PLEASE HELP!!!! WRITE AN EXPRESSION

Answers

Answer:

10c + 5b + 420 + 4c

Step-by-step explanation: 10 dollars for each child, 5 dollars per a pair of rubber boots, party room is 420 and 4 is per each child's pizza

Find the value of x in the triangle shown below.

1. x = 3
2. x = √20
3. x = 2
4. x = √36

Answers

Step-by-step explanation:

5²=4²+x²

25=16+x²

25-16=x²

9=x²

√9=√x²

3=x

A

Alfonso scored 18 points during his last basketball game,which was 40% of the points the entire team.
the entire team score________points.​

Answers

Answer:

45 points

Step-by-step explanation:

40/100=18/x    equation

100×18=1800     multiply

1800÷40=45     divide

x=45 points

Answer:

48 points

Step-by-step explanation:

I took the test

pls help i dont understand

Answers

Answer:

D and C should be correct.

Step-by-step explanation:

Included picture
Question is not hard so please answer correctly

Answers

It can sometimes be rational

A tool box has the dimensions of 10 in by 4 in by 3 in. If Andrea plans to double one dimension to build a larger tool box, she believes she would double the volume of the tool box. Is she correct?

Answers

Answer: Yes

Step-by-step explanation:

Given

Dimension of the toolbox is [tex]10\ in.\times 4\ in.\times 3\ in.[/tex]

suppose the length of the box is doubled, then a new length will be [tex]2\times 10\ in.[/tex]

So, the volume of the box becomes

[tex]\Rightarrow V=2\times 10\times 4\times 3[/tex]

It can also be written as

[tex]\Rightarrow V=2\times (10\times 4\times 3)=2\times (V_{old})[/tex]

i.e. the volume of the toolbox is doubled. Therefore, Andrea is correct.

Which of the following represents the graph of f(x) = 3x + 1?

Answers

Answer:

the answer is the top one

Step-by-step explanation:

the +1 is on the y axis. y=mx+b

mx=3x     b= +1    the b is always on the y-axis

hope this helps :))

Evelyn is going to invest $3,500 and leave it in an account for 16 years. Assuming the
interest is compounded quarterly, what interest rate, to the nearest tenth of a
percent, would be required in order for Evelyn to end up with $6,200?

Answers

Answer:3.6%

Step-by-step explanation:

What are the integer solutions to the inequality below? 2 x < 3 x + 2 ≤ x + 6

Answers

Answer:

-2 < x ≤ 2

Step-by-step explanation:

Inequality form: -2 < x ≤ 2
Interval Notation: (-2, 2)
Thus the answer is: (-2, 2) or -2 and 2

PLEASE PLEASE SOMEONE HELP WITH THIS QUESTION!! 15 POINTS AND I WILL AWARD BRAINIEST!!!!

Answers

Answer:

x=14

Step-by-step explanation:

complementary=90 degrees

4x+2x+6=90

6x=84

x=14

what is the volume to the composite figure.

Answers

Answer:

462 [tex]cm^{3}[/tex]

Step-by-step explanation:

Rectangular Prism:  7 x 8 x 6 = 336

Triangular Prism: (0.5 x 7 x 6) x 6 = 126

336 + 126 = 462


A ship is 130 m away from the centre of a barrier that measures /
180 m from end to end. What is the minimum angle that the
boat must be turned to avoid hitting the barrier?

Answers

Answer:

Step-by-step explanation:

50 meters away

DO it and thanks for the helpppp!!!!!!!!!!!!!!

Answers

Answer:

c

Step-by-step explanation:

the height is 3 so multiply everything by 3 (AFTER) THEN you add the 2 and 5 and get 10 then times by the 3 to get 30

Write the word sentence as an inequality. A number z is fewer than 3/4.

Answers

Answer:

[tex]z<\frac{3}{4}[/tex]

Step-by-step explanation:

Please look at the picture I have been stuck on this question and I would really appreciate it if you can help me thank you

Answers

Answer:

52 feet

Step-by-step explanation:

distance is 6 from the question

6 = 5/6 √h

6/5 (6) = √h

36/5 = √h

7.2 = √h

7.2x7.2 = h

h = 51.84

this is Apx huh?

What is 714.29+98.65

Answers

The answer is 812.94

Answer:

812.94

Step-by-step explanation:

make sure to line up the decimal to each other to make sure the decimal is in the right place

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