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How to do simultaneous equations

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Simultaneous equations – Higher

Sometimes you will be asked to find 2 unknown values by solving 2 equations at the same time. These types of equations are called simultaneous equations.

Simultaneous equations

Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.

The first step is to try to eliminate one of the unknowns.
Example

Solve these simultaneous equations and find the values of x and y.

* Equation 1: 2x + y = 7
* Equation 2: 3x – y = 8

Add the two equations to eliminate the ys:

* 2x + y = 7
* 3x – y = 8
* ————
* 5x = 15
* x = 3

* Now you can put x = 3 in either of the equations.
* Substitute x = 3 into the equation 2x + y = 7:
* 6 + y = 7
* y = 1

So the answers are x = 3 and y = 1

Sometimes you will need to multiply one of the equations before you can add or subtract. Have a look at the activity below.

On other occasions you will need to multiply both equations to find the unknown values. Always look for a way to cancel out one of the unknown terms. Have a go at the question below.

Question

* Solve the two equations:
* Equation 1: 2a – 5b = 11
* Equation 2: 3a + 2b = 7

Answer

* 4a – 10b = 22 (Multiply by 2)
* 15a + 10b = 35 (Multiply by 5)
* ———————-
* 19a = 57 (Adding)
* a = 3

* Put a = 3 into the equation 3a + 2b = 7:
* 9 + 2b = 7
* 2b = -2
* b = -1

So the answers are a = 3 and b = -1.

We can also use a method of substitution. Look at the following example:
Example

Solve the simultaneous equations:

Equation 1: y – 2x = 1

Equation 2: 2y – 3x = 5

Rearranging Equation 1, we get y = 1 + 2x

We can replace the ‘y’ in equation 2 by substituting it with 1 + 2x

Equation 2 becomes: 2(1 + 2x) – 3x = 5

2 + 4x – 3x = 5

2 + x = 5

x = 3

Substituting x = 3 into Equation 1 gives us y – 6 = 1, so y = 7.

Solving simultaneous equations using graphs

Solving simultaneous equations using a graph is easier than you might think. First, you need to draw the lines of the equations. The points where the lines cross is the solution.
Linear equations

The graphs of linear equations will give straight lines.
Example

* Solve these simultaneous equations by drawing graphs:
* 2x + 3y = 6
* 4x – 6y = – 4

For example, to draw the line 2x + 3y = 6 pick two easy numbers to plot. One when x = 0 and one where y= 0

* When x = 0 in the equation 2x + 3y = 6
* This means 3y = 6 so y = 2
* So one point on the line is (0, 2)

* When y = 0
* 2x = 6 so x = 3
* So another point on the line is (3 ,0)

In an exam, only use this method if you are prompted to by a question. It is usually quicker to use algebra if you are not asked to use graphs.
image: graph showing 2x + 3y = 6 and 4x minus 6y = minus 4

Linear and quadratic equation
Example

* Solve the simultaneous equations by drawing graphs.
* y – 2x = 1
* y = x2 – 2

Simultaneous Equations

A pair of “Simultaneous equations” is two equations which are both true at the same time. You have two equations which have two unknowns to be found.
Example

A man buys 3 fish and 2 chips for £2.80
A woman buys 1 fish and 4 chips for £2.60
How much are the fish and how much are the chips?

First we form the equations. Let fish be f and chips be c.
We know that:

3f + 2c = 280    (1)
f + 4c = 260      (2)

There are two methods of solving simultaneous equations. Use the method which you prefer:
Elimination

This involves changing the two equations so that one can be added/ subtracted from the other to leave us with an equation with only one unknown (which we can solve). We can ‘change’ the equations by multiplying them through by a constant- as long as we multiply both sides of the equation by the same number it will remain true.

In our above example:

Doubling (1) gives:
6f + 4c = 560 (3)

Since equation (2) has a 4c in it, we can subtract this from the new equation (3) and the c’s will all have disappeared:
(3)-(2) gives 5f = 300
∴ f = 60
Therefore the price of fish is 60p

So we can put f=60 in either of our original equations. Substitute this value into (1):
3(60) + 2c = 280
∴ 2c = 100
c = 50
Therefore the price of chips is 50p
Substitution

The method of substitution involves transforming one equation into x = (something) or y = (something) and then substituting this something into the other equation.

So,

Rearrange one of the original equations to isolate a variable.

Rearranging (2): f = 260 – 4c
Substitute this into the other equation:
3(260 – 4c) + 2c = 280
∴ 780 – 12c + 2c = 280
∴ 10c = 500
∴ c = 50
Substitute this into one of the original equations to get f = 60 .
This section is higher tier Harder simultaneous equations

To solve a pair of equations, one of which contains x2, y2 or xy, we need to use the method of substitution.
Example

2xy + y = 10  (1)
x + y = 4        (2)
Take the simpler equation and get y = …. or x = ….
from (2), y = 4 – x    (3)
this can be substituted in the first equation. Since y = 4 – x, where there is a y in the first equation, it can be replaced by 4 – x .
sub (3) in (1), 2x(4 – x) + (4 – x) = 10
∴ 8x – 2×2 + 4 – x – 10 = 0
∴ 7x – 2×2 – 6 = 0
∴ 2×2 – 7x + 6 = 0  (taking everything to the other side of the equals sign)
∴ (2x – 3)(x – 2) = 0
∴ either 2x – 3 = 0 or x – 2 = 0
therefore x = 1.5 or 2 .

Substitute these x values into one of the original equations.
When x = 1.5,  y = 2.5
when x = 2, y = 2


ResourceS:-

How to do a works cited page for a book

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How to Make Works Cited Page ?

Begin your Work Cited page on a clear sheet and center the words
“Work Cited” on the top line of the page.

Your page should include 1-inch margins and follow the same header format as the rest of your paper.

Double-space all citations, and create hanging indentations on all second and subsequent lines of each citation.

Each new citation should begin at the margin.

Alphabetize your citations by author’s last name, and make sure your capitalization and punctuation are appropriate.

Use italics or underline the titles of large works, such as books and magazines Use quotation marks for poems and articles.

If your reference has no listed author, list the book alphabetically by the book’s title.

List the page numbers to refer the reader to the page on which you obtained your quotation or information.

Format each entry on your Works Cited page according to the style standards your instructor requires.

One of the most commonly used styles is the Modern Language Association style.

To conform with MLA style, list the author’s last name, then first name, and separate the names by a comma The first name should be followed by a period Enter the title of the book.

Underline or italicize the book’s name, and follow it with a period. Enter the name of the book’s place of publication and then a semicolon. List the name of the publisher, follow it with a comma, then list the year of the book’s publication.

End the citation with a period Your citation should look something like this:

AuthorLastName, Firstname. Title of Book Boston: Random House, 2009.

If the book has more than one author, list the names in alphabetical order and follow the same format:

Brown, John, and James Author The Title of Book. Boston: Random House, 2009.

If the book has an edition, you must list the edition information after the title of the book:

Brown, John, and James Author The Title of Book about Citation 5th ed. New York: Random House, 2009.

Books without authors and pamphlets should be cited in the same manner:

Title for a Pamphlet or Book Without an Author Washington: Random House, 2009.

Dissertations may be cited even if they have not yet been published. They should include the abbreviation “Diss” and the university:

Brown,John J. Dissertation on the Appropriate Way to Create a Works Cited Page Diss. University of Higher Learning of Works Cited, 2006. New York: Random House, 2009.

image of Any books you use in writing a paper should be included in your Works Cited page

Research papers and term papers require that you cite your reference information on the Works Cited page.
The Works Cited page should appear at the end of your paper and start on a separate sheet.
The page will include the name of the books or other resources you used, as well as information enabling your reader to easily refer to your sources.
the sources:

http://www.ehow.com

http://owl.english.purdue.edu

http://www.studyguide.org

How to do a wire transfer

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How to Do an International Wire Transfer ?

Contact the foreign bank and collect the following information:

1.Name of Bank
2.Bank Identifier Code (BIC)
3.Full address of the bank or branch address
4.IBAN # if sending to Europe

Collect the following information from the beneficiary of the funds:

1.Name
2.Account number
3.Complete address

Determine the amount of money you wish to send Ensure the availability of the funds in your account.

Remember,usually there is a fee for each international wire transfer. Shop around credit union banks for a good rate.

After sending the wire, ask for a confirmation Collect necessary information to track the wire transfer.

Also ask the beneficiary bank for an email or fax confirming the receipt of funds.

Wire transfer or credit transfer is a method of Electronic funds transfer from one person or institution (entity) to another.

A wire transfer can be made from one bank account to another bank account or through a transfer of cash at a cash office.

Wire transfer systems are intended to provide more individualized transactions than bulk payment systems such as ACH and Check21.

picture of Do an International Wire Transfer

A wire transfer helps to move money from one account to another account.
The convenience of not having to physically move the funds is unbeatable Below are simple step by step instructions for wiring your money.

the sources:

http://www.ehow.com

https://www.wellsfargo.com

http://en.wikipedia.org

How to do a works cited

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How to Do Works Cited ?

Collect all of the cited work Make sure that all of the information is available to include on the works cited page.

Review appropriate styles Many academic departments direct students toward a particular format These include MLA, APA and Chicago styles.

Buy or borrow style manuals All of the major styles have their own guides or manuals that students and others can use to adhere to a specific format for works cited.

Look at elements like double spacing, alphabetization and more for the works cited section of a paper These are common formats that many instructors and academic programs demand.

Students can get more information through careful reading of style guides for skills that will benefit them later in an academic career.

Review the syllabus if your works cited page is for an academic course. Most academic instructors include a paper syllabus at the beginning of a course.

The syllabus lists most of the assignments and may provide helpful information about how to comply with specific rules from a program or professor.

Look through the syllabus for any information on how the works cited section of a paper should be done.

Many instructors have their own preferences, and these may or may not be included on the syllabus. If they are not found on the syllabus, students can ask instructors directly about how they want a works cited section to look.

Write works cited entries For each work that has been cited, include a specific line with author, publisher and other information as necessary, including pages and more.

Review the works cited page to make sure that all of the appropriate information is included.

Check citations and footnotes. Make sure that these are correctly marked on the paper so the reader can find his way from a citation or footnote to the works cited page, where he will find information on the research materials that provide a basis for the research paper or project.

How to Make Works Cited Page ?

Begin your Work Cited page on a clear sheet and center the words “Work Cited” on the top line of the page.

Your page should include 1 inch margins and follow the same header format as the rest of your paper.

Double space all citations, and create hanging indentations on all second and subsequent lines of each citation.

Each new citation should begin at the margin.

Alphabetize your citations by author’s last name, and make sure your capitalization and punctuation are appropriate Use italics or underline the titles of large works, such as books and magazines.

Use quotation marks for poems and articles If your reference has no listed author, list the book alphabetically by the book’s title.

List the page numbers to refer the reader to the page on which you obtained your quotation or information.

Format each entry on your Works Cited page according to the style standards your instructor requires.

One of the most commonly used styles is the Modern Language Association style.

To conform with MLA style, list the author’s last name, then first name, and separate the names by a comma. The first name should be followed by a period Enter the title of the book.

Underline or italicize the book’s name, and follow it with a period. Enter the name of the book’s place of publication and then a semicolon. List the name of the publisher, follow it with a comma, then list the year of the book’s publication.

End the citation with a period. Your citation should look something like this:

AuthorLastName, Firstname. Title of Book. Boston: Random House, 2009.

If the book has more than one author, list the names in alphabetical order and follow the same format:

Brown, John, and James Author The Title of Book. Boston: Random House, 2009.

If the book has an edition, you must list the edition information after the title of the book:

Brown,John, and James Author The Title of Book about Citation 5th ed. New York: Random House, 2009.

Books without authors and pamphlets should be cited in the same manner:

Title for a Pamphlet or Book Without an Author Washington: Random House, 2009.

Dissertations may be cited even if they have not yet been published. They should include the abbreviation “Diss” and the university:

photo of Any books you use in writing a paper should be included in your Works Cited page

Research papers and term papers require that you cite your reference information on the Works Cited page The Works Cited page should appear at the end of your paper and start on a separate sheet.
The page will include the name of the books or other resources you used, as well as information enabling your reader to easily refer to your sources.

the sources:

http://www.ehow.com

http://www.wikihow.com

http://ksuweb.kennesaw.edu

How to do a virus scan on a mac

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How to Check your Mac for a Virus ?

Purchase an antivirus software This antivirus software, such as McAfee VirusScan for Mac (be sure you purchase it for Macs), costs money but is great for detecting viruses on Macs.

The software can be downloaded onto your computer where you can use it to run a virus scan Some programs even detect viruses without the need for scan run.

For those who don’t want to pay the price, download free antivirus software such as ClamXav.

Though not as sophisticated as the priced antivirus software (which you should get if you are seriously worried about your Mac) the ClamXav does a great job for a zero-cost product.

End note.
To best avoid a virus do not download software from unaccredited or lesser known sites Adult sites,free movie and television sites, and others that entice you to download ANYTHING are possible risks.

To figure out what’s safe, research the sites you want to visit before loading them Sometimes getting hit with a virus is unavoidable

malware writers (or “script kiddies”) are sneaky and smart.

How to Avoid Downloading a Virus from Limewire ?

Think about what it is that you want to download.

Make sure that the content you are downloading is legal.

Realize that searching for a game on Limewire usually results in an average of 50-70% of content to be a virus.

Your game will probably be much larger than a virusSo as a general rule of thumb,anything that’s claiming to be a game but is less than5MB in size is most likely a virus.

Realize that music has a camouflage virus. For example, if you type “Temmperaturree-Sean Paul” (Mistakes and all) a camouflage virus will be a search result and it will read.

“Temmperaturree Sean Paul” as opposed to a real song which will read “Temperature Sean Paul” and if you move the mouse over it you will see the year,CD it is from and other information; you will see nothing about the “song” when it is a camouflage virus.

Do not download any file types that you do not want, so if you want an mp3 music file, don’t be downloading any exe files. Remember click the tab to search for Music only.

Know that it depends on the size for programs If it’s a small program like Trayit (a program that will minimize programs into the system tray) or Artmoney (a game cheat program), you’ll have to only download the zip or rar files and scan them for viruses.

For larger programs you can usually follow the same rule of thumb for games.

Also look for the BitRate for Music If there’s no BitRate in a music file, there’s no music in the file It means that it is a virus Videos and Software don’t have BitRates.

Another thing to do when you download a file, for example Mp3′s, rightclick at the bar at the top (that’s the info bar), select the “length” option, and again, check if it has any length available, if not, it’s probably a virus, and if it’s ABOVE the exact length, e.g. your song is typically 2 to 3 minutes, but if the file is 23 minutes, that’s probably a virus.

Look at how the file is displayed, most likely but not always the ones that aren’t capitalized are viruses.

If you do download a file look at the status, if it is going unusually fast it might be a virus.

photo of Check your Mac for a Virus

In Software Land, Macs are notoriously “virus proof” Unfortunately, the reputation has given millions of Mac owners a false sense of security Macs rarely get viruses because
most malware lurking about is geared towards the Windows Operating System and Macs are built upon the very solid UNIX core (which I will not go into) In the end, Macs are simply virus “resistant” which means your Mac could eventually be affected Here’s what to do if you want to make sure that hasn’t happened yet:

the sources;

http://www.ehow.com

http://www.wikihow.com

http://tech.its.iastate.edu

How to do a video response

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How to Post a Video Response on Youtube ?

Youtube is one of the most popular and frequently visited websites in the world People have the ability to upload videos of themselves, things they have taped or material they have taken from other sites.

Other people also have the option to respond to videos with their thoughts on the material They can respond in several different ways, including a video response.

Go to the Youtube homepage.

Log in to your Youtube account. If you do not have an account with Youtube service, create one in order to post a video response.

Choose a video to watch from those displayed on the homepage or type in a topic of interest in the subject line at the top of the screen.

Watch the chosen video.

Click the “Post a Video Response” link at the bottom right of the video box.

Choose between the “Record a Video,” “Choose a Video” and “Upload a Video” options.

Follow the instructions for whichever option you choose and your video will appear in the comments section underneath the video box.

A YouTube Video Account
a Pre-Recorded Video Uploaded To your computer

the sources:

http://www.ehow.com

http://www.wikihow.com

http://www.carlblemming.com

how to do a vlookup

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How to Do a VLOOKUP With Two Spreadsheets in Excel ?

The VLOOKUP functon in Excel looks for a certain entry in the first column of a vertically oriented table After it finds the row with the first match, it finds the column you specify in the function.

The function then returns the cell contents of that row and column from the searched table.

You may need to perform such a search through a separate spreadsheet in the same workbook This makes the syntax only slightly more complex.

Select the cell in which you want the returned value.

Click on the formula bar, the long empty box at the top of the screen.

Type =VLOOKUP(“text you want to match”,Be sure to include the double quotes.

Click the tab of the other spreadsheet, the one holding the searchable table.

Highlight the table.

Click back to the original spreadsheet Now the location will be in the VLOOKUP function.

Click the formula bar again,add a comma after the table location and type in which column you want the value returned from. For example,if you want to return two columns to the right of the search column,type 3.

Type a closing parenthesis and press “Enter.”

In a blank cell, type =VLOOKUP(lookup_value,table_array,col_index_number,Range_lookup) where:

lookup_value is the value you want to identify
table_array is the range of the table you are searching.

col_index_number is the column number in the table that you are searching.

Range_lookup is whether you want an exact or approximate match.

The values can be true (or omitted) or false.
If this is set to false, you can use wildcard characters (? or *) to broaden your search.

image of Use Vlookup With an Excel

VLOOKUP is a function that searches for a specified value vertically down the first column of an array When the value is found,VLOOKUP searches across to a specified column and enters the value of the cell.

the sources:

http://www.contextures.com

http://www.wikihow.com

http://www.ehow.com

How to do a urinalysis

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How to Use Urinalysis to Detect Bulimia ?

Get a urine sample from the patient Ask a parent or nurse to observe the patient entering and exiting the bathroom to ensure that the sample is not tampered with, but be sure to respect the privacy of the patient as well.

The testing may be done at a different office if the primary doctor’s location is not equipped to perform a urinalysis.

Screen the urine sample for red and white blood cell counts Red blood cells in the urine can be the result of strenuous activity and white cells could indicate an internal infection.

Additional blood tests may be required to check for anemia.

Look for protein and ketone traces during the urinalysis These substances are not normally found in urine and can be signs of serious kidney problems caused by bulimic behavior.

Sick kidneys will also allow traces of sugar into the person’s urine.

Check the pH level of the patient’s urine sample A normal person has a pH that generally ranges from 5.5 to 7.5. A reading that is outside of this range could be indicative of kidney problems resulting from bulimia.

Examine the specific gravity of the urine.

This test will detect the amount of solid substances in the urine and will show if bulimia is causing dehydration.

Speak to the patient about the urinalysis results and explain how bulimia is causing problems for the his body.

Certain medications and an increased amount of water can help the patient avoid permanent damage to the kidneys, but continued bulimia will only make it worse.

How to Pee for a Clean Catch Urinalysis for Women ?

Wash your hands. Be sure to follow the basics on hand washing.

Undress. Remove your pants and underwear.

Sit on the toilet with your legs spread apart as far as possible.

You don’t have to spread your legs super far, just as far as you feel comfortable with.

Using your first and second fingers, spread apart your labia (the folds of skin around the urinary opening).

Your fingers should be shaped like an upside down letter V. Stay like this for the rest of the procedure.

Clean around the urinary opening. With the first wipe, wipe from front to back down the middle with the other two, wipe each side.

Start urinating into the toilet.

After about a second, hold the cup under the stream of urine while still holding your labia.

When you have finished peeing, place the cover on the cup.

If you are collecting the sample at home and cannot get it to a lab in an hour, refrigerate it.

photo of Use Urinalysis to Detect Bulimia

Bulimia can cause several nutritional deficiencies in patients.
A wide-ranging examination must be used to screen for all possible damage from the eating disorder once it has been diagnosed.
You can use a urinalysis to detect thyroid and kidney damage resulting from bulimia It is a simple matter with a few important guidelines.

the sources:

http://www.ehow.com


http://www.wikihow.com

http://www.labtestsonline.org

How to do a upside down question mark

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How to Make an Upside Down Question Mark on Microsoft Word ?

Although Microsoft Word handles text and all of its characters just like any other word processing program,the software shows its limitations against desktop publishing programs that allow features such as upside down text.

While Word doesn’t have any kind of keystroke to provide upside down text, users will find a quick workaround does the trick.

Use upsidedown text for writing items such as questions in Spanish, or just to add an off kilter element to your next Word document.

Open Microsoft Word Click the “Insert” tab Click the “Text Box” tab on the ribbon.

Select the first option, “Simple Text Box,” and it is inserted onto the document.

Click into the placeholder text and type a question mark The rest of the placeholder text is deleted.

Resize the box to fit just the question mark by dragging its right end in toward the question mark.

Click the text box’s border to open the new orange “Text Box Tools” tab and ribbon at the top of the screen. Click the “Shape Fill” button and select “No Fill” Click the “Shape Outline” button and select “No Outline” You are left with just the question mark, but it is still right-side up.

Click the question mark to re-open the text box it is still in even though the box is not visible.

Click on and twirl the small green dot in the box’s top center.

Twirl 180 degrees until the question mark is upside down, then click off the text box onto the Word document.

Improper keyboard use can result in carpal tunnel syndrome.

photo of question mark

photo of question mark

As ever, please do NOT post your answers, but do say if you think you have solved it and how long it took.  Answer on Monday!


the sources:

http://fsymbols.com

http://www.wikihow.com

http://www.ehow.com

How to do a three way call

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How to Make a 3 Way Phone Call ?

Sometimes when you are talking to another person you find the conversation is about a friend who neither of you have seen in a while.

You can get this person on the phone right away so he can talk to both of you by using the three-way phone call feature.

Advise the other person that you will call the third person and activate the three way calling feature.

Place the existing call on hold by depressing the “flash” button located on your phone Your existing caller is now on hold.

Depress the phone on/off hook, if you phone does not have a “flash” button.

Depress the phone hook and quickly release it so you do not disconnect your caller This will place that call on hold.

Listen for the dial tone.

Dial the phone number of the person you want to add to your three way call When the person answers tell them you are going to hold a three way call.

Press the flash button now and all three people are on the call.

Click the phone hook quickly if you used this method Make sure you do this quickly to avoid disconnecting your parties.

All three people are now on the call.

photo of Make a 3 Way Phone Call

Three way calling is a great way for three people to talk when they’re apart Nearly all phones are capable of making three way calls Want to connect to two of your friends at the same time, but don’t know how?

the sources;

http://www.ehow.com

http://www.wikihow.com

https://motorola-global-eng.custhelp.com