How to solve Simultaneous Equations?

Question

Before anyone says "Try Google moron!" I have looked and I can't find one with this type of equation. And all of my homework is simultaneous equations so I am finding it it hard to answer the first one. However if I can understand how the first one works, I can understand the rest, so bare with me. I wasn't in class for this lesson, I was doing operation Monserrat so I really don't get this equation:

Solve the following simultaneous equations- 2x+3y=9 and 3x+2y=1
I don't even know where to start, so show me how to do it please so I can understand the rest. P.S. It's GCSE grade. Thanks.

Answer 1

2x+3y=9 and 3x+2y=1

-----------------------------------------------

(2x+3y=9) x 3



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

---------------------------

multiply them out



6x + 9y = 27 and



-6x -4y = -2

------------------------

add them together



9y -4y = 27 -2



combine terms



5y = 25



y = 5

Answer 2

Simultaneous equations are two (or more) equations where they have the same variable(s) represented by the same letter(s). We'll use your problem as an example. In the equations: 2x+3y=9 and 3x+2y=1, it means that for both of the equations x represents the same number and that goes for y also. In this case, x=-3 and y=5. You can see what I mean by looking at the equations again. (2 x -3) + (3 x 5) = 9 and (3 x -3) + (2 x 5) = 1. Here's a link to a site that has a few different methods for solving simultaneous equations as well as a simultaneous equation calculator:



http://www.idomaths.com/simeq.php#elimination (i know it's not hyperlinked but just copy and paste it in the url and you'll be alright.



i hope this helps! :)

Answer 3

x = -3,





y = 5

Answer 4

I am a math teacher from America but I think (since you mentioned GCSE and I tutor 3 students in UK) you are in UK.....



I teach my students a method that is not in any book I have seen. They can just write down the answer

Let me know if you are interested in learning it. Then FIRST amaze your friends and teacher(s) and SECOND teach it to them



2X + 3Y = 9

3X + 2Y = 1



(-(-15) / -5 , -25 / -5 ).............(-3 , 5).......You just saw all my work



Mathcerely, Robert Jones "Teacher/Tutor of Fine Students"

Moved Florida to France June 2011 but still tutor world-wide (USA , UK ,

France , Checz Republic ...) free using Skype. If you need me to explain

further or any other math problem just let me know how to get in touch.



********* A PRESENT FOR YOU

Ask someone to write a number, say a five-digit number.

(Can be a 2-digit.....3-digit.....4-digit....ect..…

Suppose the number written is

57836

Now, without showing the asker, you write a number on

a sheet of paper and keep it folded. You have to write the

number by subtracting 2 from the above number and

adding 2 in front which will be....

257834

Next, ask the person to write another five-digit number

below his original number. Suppose he writes 37589.

So you now have...

57836

37589

Now you write a five-digit number below it in such a

way that each digit is 9 minus digit above. You now have...

57836

37589

62410

Ask the person to add one more 5-digit number. If he

adds 54732, you add below it 45267. Note that you decided

the number by subtracting each of his digit from 9.

Thus, you now have.....

57836

37589

62410

54732

45267

Next, ask him to add all the number and he gets 257834

Show him the number which you had written as an answer

to this addition earlier in the folded paper and surprise him.