Question

help please will medal and fan

Answer 1

what is the following solution of the following system
3x+3y=10
-9x-9y=-30

Answer 2

what happens if you multiply the first equation by \(*-3\) all the way across?

Answer 3

what do you mean? @satellite73

Answer 4

multiply all terms in the first equation by \(-3\)

Answer 5

wait im a little confused what would that look like?

Answer 6

what does minus three look like?

Answer 7

-3

Answer 8

ok so multiply \[-3(3x+3y)=10\times (-3)\]

Answer 9

so 9x+9=-30

Answer 10

no

Answer 11

-30x

Answer 12

Hey @song_of_the_sole , I helped someone with a similar question earlier. You can have a read of the conversation if you like.
Link: http://openstudy.com/study#/updates/581924f7e4b03ac563213d41

Answer 13

thank you but in order for me to understand i need someone to help me like step by step @harman.singh like how @satellight73 is

Answer 14

but if u can help me step by step please do

Answer 15

okay. In general, do you know how to use the elimination method to solve a set of equations?

Answer 16

kinda but need to refresh but im sure ill catch on as we go

Answer 17

The idea is to have a common value in both of the equations so they can cancel out when subtracting.

Have a quick read of this webpage if you need to refresh on it: http://mathsfirst.massey.ac.nz/Algebra/SystemsofLinEq/EMeth.htm
Once you understand it, it will be easier for me to help you with your question

Answer 18

okay so how should we start

Answer 19

So here are our two equations
3x+3y=10
-9x-9y=-30

Lets begin by multiplying each of the equations by a number which would give us the same x value in both equations

Answer 20

Lets aim to have -9x in both of the equations

Answer 21

so 3

Answer 22

Think again. Multiplying 3 by the first equation would give us 9x. But we want -9x

Answer 23

-3

Answer 24

Yes, thats correct. Now multiply the whole equation by -3 and what do you get?
-3(3x+3y=10) = ?

Answer 25

-9x-9y=10

Answer 26

You also need to multiply the 10 by -3.

So it now looks like -9x-9y=-30

Answer 27

oh sorry

Answer 28

so now what?

Answer 29

Now that we have managed to get the same coefficients for the x value, we can subtract them from one another. It would look like:

-9x-9y=-30
-(-9x-9y=30)

What do you get after subtracting them from one another?

Answer 30

what do you mean?

Answer 31

Have a look at that website again. See how they did step 2. Do you understand that part?

Answer 32

not really

Answer 33

Once they had it in this order,
6x + 9y = 24
-(6x + 4y = 14)

They multiplied the bottom equation by - (negative) to expand the bracket
So it became -6x-4y=-14. Good so far?

Once I write the equations again, they look like
6x+9y=24
-6x-4y=-14

Now solve each of the values one by one
6x take away 6x is 0 (zero) so they cancel out.

You are now left with
9y=24
-4y=-14

9y take away 4y gives you 5y.

and 24 take away 14 gives you 10

Now we are left with
5y=10

Rearranging this we can find the value for y
y=10/5

Therefore y=2

Do you understand what I explained? We have to use a similar approach to our question

Answer 34

Let me know if you want me go over anything specific from the above example. It might look confusing at first

Answer 35

okay so how should i do this for my equation... so sorry but i really need to speed this up because im about to leave to get dropped off at school

Answer 36

alright I will make it quick

Answer 37

-9x-9y=-30
-(-9x-9y=-30)

After expanding the brackets, we have
-9x-9y=-30
9x+9y=30

-9x + 9x = 0 (so they cancel out)
-9y + 9y = 0 (so they cancel out)
-30 + 30 = 0 (so they cancel out)

So really, you are left with 0=0
This means that your set of equations have no solutions.
What a bugger :)

Answer 38

and thats it?

Answer 39

Yes, thats it :)

Answer 40

This one was a bit different as it had no solution. But if you understood the procedure, you will be able to solve equations that do have a solution. If you get stuck, refer to the website or ask here. Good luck!

Answer 41

Correction:
I wrote that the set of equation has no solutions. That's incorrect. I should have said the equations have infinite solution. My apologies.

For future reference,
- when the answer is 0=0 , it has infinite solutions
- when the answer is something like 0=5, it has no solutions
- when the final answer for the the coordinates is something like (5,6), it has one solution