1. Which would be a more helpful for solving the system: adding the two equations or subtracting
one from the other? Explain your reasoning.
2. Solve the system without graphing. Show your reasoning.

2x+1/2y=7
6x-1/2y=5

Answers

Answer 1

Answer:

1) Subtracting one from the other

2) x = 0.375 and y = 0.125

Step-by-step explanation:

Equation 1 :

[tex]\frac{2x+1}{2y}=7\\\\[/tex]

Equation 2:

[tex]\frac{6x-1}{2y}=5[/tex]

To solve these equations by the Elimination method we multiply equation 1 with 6 and multiply equation 2 with 2 so now,

[tex]\frac{2x+1}{2y} =7\\\\2x+1=14y\\\\Multiplying\ Equation\ 1\ with\ 6\\\\12x+6=84y[/tex]

Now for the second equation:

[tex]\frac{6x-1}{2y}=5\\\\6x-1=10y\\\\Multiplying\ equation\ 2\ with\ 2 \\\\12x-2=20y[/tex]

Now subtracting equation 2 from equation 1

[tex]12x+6=84y\\\\12x-2=20y\\\\Subtracting\ leads\ to\\12x-12x+6-(-2)=84y-20y\\0+8=64y\\8=64y\\8/64=y\\0.125=y[/tex]

now insert this value of y into any equation

lets insert it into equation 1

[tex]\frac{2x+1}{2y} =7\\\\2x+1=14y\\2x+1=14(0.125)\\2x+1=1.75\\2x=1.75-1\\2x=0.75\\x=0.75/2\\x-0.375[/tex]


Related Questions

Please help me with this

Answers

Answer:

B.  $19

Step-by-step explanation:

Approximate prices:

1/4 lb ham = 0.25 * $6 = $1.50

1 1/2 lb turkey = 1.5 * $5 = $7.50

1 lb roast beef = $7

3/4 lb bologna = 0.75 * $4 = $3

Add the approximate individual prices:

$1.50 + $7.50 + $7 + $3 = $19

After riding a bike for 20 min you burn 190 calories. If you ride the bike for 45 minutes how many calories will you burn? Use a proportion to solve.

Answers

Multiple 20 times 45 and you get 900

A b c or d will mark for brainiest

Answers

Answer:

C

Step-by-step explanation:

Small tier will serve 20 and medium tier will serve 40

i forgot what 25 divided by 12 is lol pls help me

Answers

Answer:

2.08333333333

Step-by-step explanation:

25/12 = 2.08333333333

The division of 25 by 12  gives the quotient 2 and remainder is 1.

What is Division?

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

Given:

We have to divide 25 by 12.

The division is as follow:

                           12| 25 | 2

                                 24

                             ______

                                  1

Thus the Quotient is 2 and remainder is 1.

Learn more about Division here:

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draw the graph of y=2x+3 on the grid

Answers

Answer:

put a point at (0, 3) and a point at (1, 5). Draw a line through these points and that if your line

Step-by-step explanation:

This is because the y-intercept(b) in the equation y=mx+b  is 3. This means the line will cross the y-intercept at (0, 3). NeXT, m is the slope and since it is a positive 2 you could rewrite it as 2/1. Because slope is rise/run just go up 2 units and over 1 unit for every new point on that line.

The graph for the equation y=2x+3 is added in the attachment.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

y=2x+3

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

Because the line crosses the y-axis at (0,y), the value of y when x is 0 is referred to as the y-intercept. The collection of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

The given equation is in the form of y=mx+c, the given form is a slope-intercept form of the line.

The line passes through the points (-1.5,0) and (0,3).

Thus, the graph for the equation y=2x+3 is added in the attachment.

Learn more about the linear equation here:

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Hans cell phone plan cost $200 to start. Then there is a $50 charge each month. Graph

Answers

The answer will be 400

Add.
7/8 + 5/6
solve step by step and give me a good explanation and then i will mark you brainliest

Answers

Answer:

Step-by-step explanation: first you add the top number which is 7 + 5=12 then you add the below numbers which is 6+8= 14 so the answer is 12/14

Answer:

7/8 x 5/5 = 40/35     5/6 x 8/8 =48/35 = 1 and something

Step-by-step explanation:

e

Miguel makes punch using 1 4/5 cups of sugar. The recipe requires 2 1/2 times as much water. How much water does the recipe call for?

Answers

(9/5)•(2.5)= 4.5 cups of water.
hope that helps!

Mass A has a mass of 10 kg while mass B has a mass of 20 kg. Which of these must be true?

Answers

Mass a because it’s shorter in weight

Need answer for this

Answers

Answer:

dukh dusri if la is aaz ex rc UV pic of x maa la is pta is is wa wa ea raaz raaz raaz tez TX UV in on on lb lg aaz wax ex ex ex un in pa pe pe la na

Step-by-step explanation:

n mn bhi lv vm mb cm kc gl of FL ek to tk tu tum

Select all the lines that have a y-intercept of -2.
-2 +4x = y
-2x + 2 = y
y = -2x + 1
y = -2x - 2

Answers

Answer:

y=-2x+1

Step-by-step explanation:

Answer:

I think its the second and fourth one

I need help someone plz help me

Answers

i believe your answer would be 1/10:))

Answer:

1/10

Step-by-step explanation:

The first step is put the number 1 under the 2.

For division you have to do KEEP CHANGE FLIP.

you keep the first fraction.

you change the operation to multiplication.

you flip the fraction.

The new expression will be: 1/5 x 1/2

Then you just multiply across like this.

1/5 x 1/2 = 1/10

The 984 km trip takes a plane 2 hours and 24 minutes when flying against the wind. The
same trip takes 1 hour and 36 minutes with the wind. How fast would the plan be in still
air?

Answers

Answer:2 hours.

Step-by-step explanation: The wind adds 24 minutes of flying time when going against it, and takes 24 minutes going with it.

help me with this pleaseee

Answers

C, the remainder is 16.

~Worth 15 points and brainliest❤️☮️~

Which section (A or B) of the roller coaster shows
positive acceleration?

Which section (A or B) of the roller coaster shows
negative acceleration?

Answers

Answer:

A

B

Step-by-step explanation:

Answer:

a

then

b

Step-by-step explanation:

Fill in the blank with numbers that make the statement true.


12 + _____ = 0


-14 + 34 = –––––––


-65 + 42 = _______

Answers

12 + -12 equals 0
-13+34 equals 20
And the last ones answer is -23

Answer:

12+(-12)=0

-14+34=20

-65+42=-23

A cell phone provider will allow you to buy a phone over time. They
require a $50 initial payment and then charge $25 per month. If the total
amount paid was represented by a function for the total amount paid over
time, what would be the y-intercept?
Aye yo someone help me out

Answers

Answer:  The y-intercept will be $50  or 50

Step-by-step explanation:

Since $50 is the initial fee, the 50 dollars will be the y intercept because it is the same as startup amount.

$50 plus $25 a month wlll be  $50 + 25x where x  is the number of months.

They all have to equal to the total cost  which will be represented by y.

y = 25x + 50  

HELP!!!!
Is there enough information to prove that the triangles are congruent?

If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.

If no, justify your answer.

Answers

Yes because if you rotated the triangle where “B” and “Z” are the same point the rest of the triangle will line up. Don’t take my word for it I’m not even sure I’m just making a guess by what I can see if that makes sense you can double check but hopefully this is useful :)

simplify the following
8*7-10+55​

Answers

Answer:

101

Step-by-step explanation:

8*7 -10+55.

First, multiplication.

8*7 is 56.

56-10+55

56-10 is 46.

46+55 is 101.

Hope this helps plz hit the crown :D

Mark brainliest and plz show your work!

Answers

Answer:

Step-by-step explanation:

11/12+10-5/6

take 12 as lcm

11+120-10)/12

121/12

9514 1404 393

Answer:

  121/12

Step-by-step explanation:

  [tex]\dfrac{11}{12}-(-10)-\dfrac{5}{6}=\dfrac{11}{12}+10-\dfrac{5}{6}\quad\text{eliminate parentheses}\\\\=\dfrac{11}{12}+\dfrac{120}{12}-\dfrac{10}{12}\quad\text{use common denominator}\\\\=\dfrac{11+120-10}{12}=\boxed{\dfrac{121}{12}}\qquad\text{combine terms}[/tex]

Can someone help me? Please and thank you! <3

Answers

Answer:

I think it would be 40?

Step-by-step explanation:

I think 40 because if I recall correctly, to find the range you must subtract the max from the min, the max being 100 and the min being 60 in this case.

If you have 6 candy bars and and you cut it in half 3 times what is the quotient.​

Answers

Answer: 48

Step-by-step explanation:

I’m pretty sure

Answer:

24 pieces

Quotient: 2

Step-by-step explanation:

This is the answer because:

1) If you cut one candy bar into half three times, there will be 4 pieces.

2) Then, just multiply 6 and 4 together to know how many pieces there are together:

6 x 4 = 24

Therefore, the answer is 24 pieces.

3) In order to find the quotient, just divide 6 and 3:

6 ÷ 3 = 2

Therefore, the quotient is 2.

Hope this helps! :D

the question is

"Triangles ABC, EFD, and GHI are all similar. The side lengths of the triangles all have the same units. find the unknown side lengths.



would be useful if you had an explanation on how you got the answer thanks this is my hw need it done by 3pm today ​

Answers

The unknown side lengths are

Large triangle 10

Medium triangle 2

Small triangle 12/5 or 2.4

Step-by-step explanation:

EFD to ABC is 0.4 or 2/5

EFD to GHI is 0.24 or 6/25

ABC to GHI is 0.6 or 6/10

The side length of c is  2.

The side length of d is 10.

The side length of e is 10.

The side length of h is  2.4.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangles ABC, EFD, and GHI are all similar.

The side lengths of the triangles all have the same units.

This means,

The ratio of the corresponding sides of the two triangles is the same.

Now,

ΔABC and ΔGHI

4/(12/5) = 4/h = c/ (6/5)

20/12 = 4/h = 5c/6

We will consider 20/12 = 4/h.

20/12 = 4/h

5/12 = 1/h

h = 12/5

h = 2.4

We will consider 20/12 = 5c/6

20/12 = 5c/6

4/2 = c

c = 2

Now,

ΔABC and ΔEFD

4/e = 4/d = c/5

4/e = 4/d = 2/5

Consider 4/e = 2/5

4/e = 2/5

2/e = 1/5

e = 10

Consider 4/d = 2/5

4/d = 2/5

2/d = 1/5

d = 10

Thus,

The side length are:

c = 2

d = 10

e = 10

h = 2.4

Learn more about triangles here:

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Sarah is a computer engineer and manager and works for a software company. She receives a

fixed annual increase in the number of projects she handles each year. She worked on 129

projects in the fourth year of her employment and 207 projects in her tenth year.

(a) How many projects did Sarah work on in her first year?

(b) If a project pays her $500 on average,

I. How much did she earn in her twelfth year?

II. How much did she earn in total in her first 12 years with the company

Answers

Answer:

a) Number of projects in the first year = 90

b) Earnings in the twelfth year = $116500

Total money earned in 12 years = $969000

Step-by-step explanation:

Given that:

Number of projects done in fourth year = 129

Number of projects done in tenth year = 207

There is a fixed increase every year.

a) To find:

Number of projects done in the first year.

This problem is nothing but a case of arithmetic progression.

Let the first term i.e. number of projects done in first year = [tex]a[/tex]

Given that:

[tex]a_4=129\\a_{10}=207[/tex]

Formula for [tex]n^{th}[/tex] term of an Arithmetic Progression is given as:

[tex]a_n=a+(n-1)d[/tex]

Where [tex]d[/tex] will represent the number of projects increased every year.

and [tex]n[/tex] is the year number.

[tex]a_4=129=a+(4-1)d \\\Rightarrow 129=a+3d .....(1)\\a_{10}=207=a+(10-1)d \\\Rightarrow 207=a+9d .....(2)[/tex]

Subtracting (2) from (1):

[tex]78 = 6d\\\Rightarrow d =13[/tex]

By equation (1):

[tex]129 =a+3\times 13\\\Rightarrow a =129-39\\\Rightarrow a =90[/tex]

Number of projects in the first year = 90

b)

Number of projects in the twelfth year =

[tex]a_{12} = a+11d\\\Rightarrow a_{12} = 90+11\times 13 =233[/tex]

Each project pays $500

Earnings in the twelfth year = 233 [tex]\times[/tex] 500 = $116500

Sum of an AP is given as:

[tex]S_n=\dfrac{n}{2}(2a+(n-1)d)\\\Rightarrow S_{12}=\dfrac{12}{2}(2\times 90+(12-1)\times 13)\\\Rightarrow S_{12}=6\times 323\\\Rightarrow S_{12}=1938[/tex]

It gives us the total number of projects done in 12 years = 1938

Total money earned in 12 years = 500 [tex]\times[/tex] 1938 = $969000

Phone Company 1 charges a flat rate of $25.00 a month for local calling,
and $0.05 per minute for each long distance call. Phone Company 2
charges a flat rate of $20.00 a month for local calling, and $0.10 per
minute for long distance calling. After how many minutes of long distance
calling do the phone companies charge an equal amount?
A 50 minutes
B. 100 minutes
C. 200 minutes
D. 300 minutes

Answers

Answer:

B = 100

Step-by-step explanation:

25 + .05x = 20 + .10x

5 = .05x

100 = x

Hi, this is Coco Quinn and I would love to mark you the brainiest if u answer my question it's 56 points!!!

Answers

Answer:

i cant see the picture it very small

Step-by-step explanation:

Answer:

I can't see it. It's too small

Step-by-step explanation:

Madison has lemons and papayas in a ratio of 3:22 how many papayas does she have if she has 12 lemons

Answers

She would have 88 papayas if she had 12 lemons

What is the next step in constructing an angle mno congruent to the given angle with a straightedge and a compass

Answers

Answer: ever got the answer?

Step-by-step explanation:

a construction crew was made up of 8 men and the rest women. if 40% of the crew were men, how many people were in the crew?

Answers

Answer:

66.66

Step-by-step explanation:

HONESTLY I REALLY DONT KNOW BUT TRY IT

I need help with this please someone help me

Answers

you use y=mx+b i think to find the total cost
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