Mathematics High School

What is the solution of the system? Use elimination.
2x + 2y +z = 7
-X – y +z = -5
x + 3y – 4z = 12

Answers

Answer 1

Answer:

The solutions to the system of the equations by the elimination method will be:

[tex]x=2,\:z=-1,\:y=2[/tex]

Step-by-step explanation:

Given the system of the equations

[tex]2x\:+\:2y\:+z\:=\:7[/tex]

[tex]-x-\:y\:+z\:=\:-5[/tex]

[tex]x+3y-4z=12[/tex]

solving the system of the equations by the elimination method

[tex]\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]-2x-2y+2z=-10[/tex]

[tex]+[/tex]

[tex]\underline{2x+2y+z=7}[/tex]

[tex]3z=-3[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]2x+6y-8z=24[/tex]

[tex]-[/tex]

[tex]\underline{2x+2y+z=7}[/tex]

[tex]4y-9z=17[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}[/tex]

Rearranging the equations

[tex]\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}[/tex]

solve [tex]3z=-3[/tex] for z:

[tex]z=-1[/tex]

[tex]\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1[/tex]

solve  [tex]4y-9\left(-1\right)=17[/tex] for y:

[tex]4y-9\left(-1\right)=17[/tex]

[tex]4y+9=17[/tex]

[tex]4y=8[/tex]

[tex]y=2[/tex]

[tex]\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2[/tex]

solve [tex]2x+2\cdot \:2-1=7[/tex] for x:

[tex]2x+2\cdot \:2-1=7[/tex]

[tex]2x+3=7[/tex]

[tex]2x=4[/tex]

[tex]x=2[/tex]

Therefore, the solutions to the system of the equations by the elimination method will be:

[tex]x=2,\:z=-1,\:y=2[/tex]

Related Questions

Graham crackers 222
Chocolate squares 888
Marshmallows 333
How many s'mores can Kora make if she has 202020 graham crackers?

Answers

Answer: 10?

Step-by-step explanation: Just divide 20/2 and you get the answer. Ight Ima head out

Answer:

2020 is innit so it cant be good lol

Step-by-step explanation:

3. Determine whether these two lines are parallel, perpendicular, or neither. 1 point
8x + y = 7, 4x + 3y = 12 *
parallel,
perpendicular or
neither

Answers

Answer:

The two lines are neither

Step-by-step explanation:

Parallel lines have equal slopes and different y-interceptsPerpendicular lines have a product of their slopes = -1The slope of a line whose equation is ax + by = c is m = [tex]\frac{-a}{b}[/tex]

∵ The equations of the lines are

8x + y = 7 ⇒ 1st4x + 3y = 12 ⇒ 2nd

∵ In the 1st equation a = 8 and b = 1

∴ m1 = [tex]\frac{-8}{1}[/tex] = -8

∴ The slope of the 1st line is -8

∵ In the 2nd equation a = 4 and b = 3

∴ m2 = [tex]\frac{-4}{3}[/tex]

∴ The slope of the 2nd line is [tex]\frac{-4}{3}[/tex]

→ By using the facts above

∵ m1 ≠ m2

∴ The two lines are not parallel

∵ m1 × m2 = -8 × [tex]\frac{-4}{3}[/tex] = [tex]\frac{32}{3}[/tex]

∴ m1 × m2 ≠ -1

∴ The two lines are not perpendicular

∴ The two lines are neither parallel nor perpendicular

Shala bought a pen on sale. She saved 17 percent of the original price of 29 dollars. About how much money did she save? A. 1 dollar B. 5 dollars C. 10 dollars or D. 20 dollars.

Answers

Answer:

B. 5 dollars

Step-by-step explanation:

17% = .17

"of" means to multiply.

29 × .17= 4.93

4.93 rounds up to 5

HELP WILL MAKE BRAINLIST

Answers

Answer:

3rd choice

Step-by-step explanation:

subtracted both sides by 2

-6/11 x (-1/6) i can’t find the answer

Answers

Answer:

1/11

Step-by-step explanation:

- × - gives a +

cancel the 6

Hope you can understand what i mean

The number of hours slept at night is related to the number of minutes spent exercising that day. A collection of data on the number of minutes spent exercising, x, and the number of hours slept, y, is shown in the table.

x 30 37 40 45 52 55 61 65 71 76
y 6.25 6 6.5 7 6.5 7.25 7.5 8 8.65 8.5
Which linear equation best models the relationship between x and y?

Answers

Answer:

the answer is A

Step-by-step explanation:

took the test

f(x) = 3x^2-х
Find f (10)

Answers

F(10)= 3(10)^2-x
F(10)= 3(100) - x
F(10) = 300- x

Imogen bought i number of invitations to send out for her party. After she sent out 19, she was left with 11. What is the
value of 1?
11
оооо
19
о 30

Answers

Answer:

30 in total that she bought

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

got it right on edg 2021

Help me plzzzz!!!!

Graph: y-3=1/2(x+2)

Answers

Answer:

Step-by-step explanation:

First you need to find the Slope Intercept form or find the point and slope.

The point is: (-2,3)

and the slope is: 1/2

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

y - 3 = 1/2x + 1

y = 1/2x + 1 + 3

y = 1/2x + 4

Slope intercept form: y = 1/2x + 4

Graph is show below ---

                                       |

                                      V

2x+3>_7 or 2x+9>11 plzzzz help meee

Answers

Answer:

b

Step-by-step explanation:

hi I I'm the explanation

Mora borrowed $4,830 from her mom. She agreed to pay a small amount each day until her debt is paid off. If she agreeed to pay $42 each day, how long will it take Mora to pay her mom back in full?

Answers

Answer:

115 days, untill she has payed her mom the full amount. plz pick me as the brainleist! XD

Step-by-step explanation:

Find the area of the rectangle.

Answers

Answer:

5m squared

Step-by-step explanation:

(m)(5m) = 5m^2

The reciprocal of y^1/2 is 5
Work out the value of y.

Answers

Answer:

y = 1/25

Step-by-step explanation:

Reciprocal of y^(1/2)  : 1/y^(1/2)

1/y^(1/2) = 5

y^(1/2) = 1/5

y = (1/5)^2

Use equivalent rates to determine the total cost for 30 pounds of Hermiston watermelons from a local farm if the farm charges $5.00 per 3 pounds

Answers

Answer:

50

Step-by-step explanation:

$5 3 $10 6 $15 9 $20 12 $25 15 $30 18 $35 21 $40 24 $45 27 $50 30

What's 2+2 WILL GIVE BRAINLIEST

Answers

Answer:

4

Step-by-step explanation:

Select the correct answer.
What is the range of the function represented by the graph?

Answers

It will be answer choice B because it’s including 2 as your y value and it’s going to infinity so it’s y greater than or equal to 1

Answer:

C. y is greater than or equal to 1

Step-by-step explanation:

The graph is above 1 on the graph. The range is along the y-axis. it ranges from 1 all the way up so it is greater than 1. The domain would be all real numbers.

What is the slope of the line passing through the points (1, 3) and (3,9)?

Answers

Answer:

3

Step-by-step explanation:

slop formula:

y2-y1

____

x2-x1

y2 is 9 and y1 is 3, so y2-y1 is 6

x2 is 3, x1 is 1, so x2-x1 is 2

6/2=3

If UW = 4x – 1 and YZ = 5x + 4, what is UW?
(I need a answer and steps to stove)

Answers

What do you mean what is UW ? There is no equation

Step-by-step explanation:

The answer is 2

You will add 2 to 4 then divide 6 by 3

Help me please!! Plz and thank uuu it’s 10 points for uu Pid Pid Pid !

Answers

It is c. If you do the equation it is -1 1/4

what is 7 1/7 - 3 5/7

Answers

Answer:

Step-by-step explanation:

7 1/7- 3 5/7= 3 3/7

3 3/7 can also be 3.42 and 24/7

A cyclist rides his bike at a rate of 10 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.

Answers

If the cyclist rides at 10mph and 1mph=1.6kph then 1.6x10=16 which means he was traveling at 16 kilometers per hour and after five hours he would have traveled 80 kilometers

plssssss it’s past due and my mom won’t get out of my hair.

Answers

Is it asking you to tell them what the numbers that the letters substitute are??

If so o might be able to help with that
What is the question asking?

The lenngths of the sides of the triangle are in the extended ratio 8:9:10. The primeter of the triangle is 108 cm.What are the lengths of the sides?
The lengths of the sides of the triangle in cm are____?

Answers

Answer:

A(8)=32cm

B(9)=36cm

C(10)=40cm

Step-by-step explanation:

let 8:9:10=A:B:C

∑ratios=8+9+10=27

Therefore lengths or triangles:-

Write the equation of the line that goes through (-3.9, -1.4) and is PERPENDICULAR to 6x + 2y = 9

Answers

9514 1404 393

Answer:

  10x -30y = 3

Step-by-step explanation:

In general form, you can start by swapping the x- and y-coefficients, negating one of them. To find the new constant for the equation, substitute the values for the given point

  2x -6y = 2(-3.9) -6(-1.4)

  2x -6y = 0.6

Multiplying by 5 will make the numbers be integers, so will put the equation in standard form.

  10x -30y = 3

what is 11x times 11y

Answers

Answer:

121xy

Step-by-step explanation:

11*11=121, x*y=xy,

121xy

Help plz!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

78.85

Step-by-step explanation:

What rate of interest compounded annually is required to double an investment in four years

Answers

Answer:

18.92%

Step-by-step explanation:

What is the factored form of the binomial expansion 81x2 + 144xy + 64y2?

(9x – 8y)2
(9x + 8y)2
(3x – 4y)2
(3x + 4y)2

Answers

(9x+8y)^2 =(9x)^2+2x(9x)x(8y)+(8y)^2

What is the probability of being born in May or on the 30th of any month?

Answers

Answer: 41/365

Step-by-step explanation:

The probability of being born in May is 31/365 (May has 31 days and there are 365 days in a year).

The probability of being born on the 30th of the month is 11/365 (11 months have at least 30 days). However, since we have included May 30 in our MAy probability, we need to use the probability of 10/365.

Add the two probabilities together, and the probability of being born in May or on the 30th is 31/365 + 10/365 = 41/365.

A scale drawing of an airplane is shown with a scale of 24 feet = 1 centimeter. What is the length of the actual plane?

Answers

Could you explain the question a little bit more

Answer:

144 feet

Step-by-step explanation:

I forgot how it is that answer but I am sure that is the answer.

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