x-3y=-9
6x+y=3

- jagr2713

x-3y=-9
6x+y=3

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- jagr2713

i dont understand this @freckles

- steve816

How does a 99 rated mathlete not know how to do system of equations O.o

- jagr2713

Well when you haven't done math in a while u forget things.....

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## More answers

- IrishBoy123

|dw:1442268783821:dw|

- jagr2713

ok i know the part where u add them and stuff but i just need help in the beginning. How do u find what to multiply them with?

- IrishBoy123

when they are set out like that, just imagine adding them and knocking out an x or a y
so,
let's do it again

- IrishBoy123

|dw:1442269218613:dw|

- jagr2713

wait why did u use 1 and 2

- IrishBoy123

if you meant, the (1) and (2) in brackets to identify the equations, and just a habit
is that what you were referring to?

- jagr2713

Because my teacher taught me to multiply them by a number and then add then and cancel the x or y u used etc

- IrishBoy123

loads of ways to do these
eg
|dw:1442269699628:dw|

- IrishBoy123

can i ask , do you work on the OS website??

- jagr2713

whats the easiest way?
can u do in equation form cause the drawing is losing me

- jagr2713

do i work on the website?

- IrishBoy123

yes

- jagr2713

what does that mean?

- IrishBoy123

are you part of the OS team?

- jagr2713

Oh yes...

- IrishBoy123

easiest way is substitution, IMHO.
as in, it's pure method.
so, from the first equation, which is \(x - 3y = -9\), you can say \(x = 3y - 9\)
then in the second, which is \(6x + y = 3\), you can say \(6(3y - 9) +y = 3\)
so \(18y - 54 + y = 3\)
or \(19y = 57\), \(y = 3\)

- IrishBoy123

so you code this site?!

- jagr2713

OOOHOHO you have to change the x-3y=*9 in x=3y-9
and lets stay relevant :D u can message me the other questions

- IrishBoy123

OK!!

- jagr2713

But what if its x+3y=-9
does 3y become positive cause u move it?

- IrishBoy123

if
x + 3y = -9
then
x = -3y - 9

- IrishBoy123

because
x+3y-3y = -9-3y

- jagr2713

so i got
6(3y-9)+y=3
18y-54+y=3
+y +y
19y-54=3
+54 +54
19y=57
y=3

- jagr2713

so now u plug it into the x too get x right?
x-3(3)=-9
x+9=-9
-9 -9
x=-18
so we got
(-18,3)

- jagr2713

??

- IrishBoy123

if you know that y = 3, plug that into one of the original equations to find x

- IrishBoy123

eg, if
x - 3y = -9
what is x
if y = 3

- IrishBoy123

or if 6x + y = 3
what is x
if y = 3??

- jagr2713

you plug it into the
x-3y=-9 right?

- IrishBoy123

into either, you want to know when they meet

- jagr2713

it says -18,3 is wrong

- jagr2713

wait don't i need another point?

- IrishBoy123

i thought we had agreed 0, 3 ?!?!

- IrishBoy123

as in x = 0

- IrishBoy123

and y = 3

- jagr2713

OOHOHOHO i did it wrong ok so i need another set of points to connect it.

- IrishBoy123

indeed you might!
gtg

- jagr2713

So how do i get it?

- jagr2713

@freckles

- IrishBoy123

really sorry @jagr2713
i gotta go sleep
i am in europe, i guess you are somewhere else
my condolensces!!!!

- jagr2713

Its ok

- jdoe0001

are you meant to solve by either substitution or elimination?

- jagr2713

Graphing them

- jagr2713

i got the answer 0,3 just need another point

- jdoe0001

well... where the graph of two equations meet, is where the answer is :)
hm if 0,3 is the answer.... isn't that what you needed? :)

- jagr2713

Yea but thats only one point need 2 for a line

- jdoe0001

hmmm one sec

- jagr2713

ok :D

- jagr2713

here use this i did another question
x-3y=-3
3x+y=1
i got (0,1)

- jdoe0001

..is that another one?

- jagr2713

Yea i just change questions
i got 0,1 but need another point

- jdoe0001

hmmm thought you were supposed to just graph them?

- jagr2713

Yea it say
solve the following system of equation by graphing them

- jdoe0001

well... I'd just graph them then :)
lemme do a quick table

- jagr2713

ok thanks

- jagr2713

wait do we just do the
x|y thing and put 0 for x and ory?

- jagr2713

|dw:1442273690049:dw|
like that?

- jdoe0001

yeap
to make a line, all you need is 2 points
so just pick two random "x" to get two "y"s

- jagr2713

OHH so
|dw:1442273743049:dw|

- jagr2713

other is
0,3 2,0

- jdoe0001

hmm yes
\(\begin{array}{llll}
x-3y=-3\implies &\cfrac{x+3}{3}={\color{brown}{ y}}
\\ \quad \\
3x+y=1\implies &{\color{brown}{ y}}=1-3x
\end{array}
\\ \quad \\
\qquad \qquad
\begin{array}{ccllll}
x&y
\\\hline\\
&\frac{x+3}{3}\\
\\\hline\\
&\frac{x+3}{3}\\
0&1\\
-3&0
\end{array}\qquad
\begin{array}{ccllll}
x&y
\\\hline\\
&1-3x
\\\hline\\
0&1\\
4&-11
\end{array}\)

- jagr2713

where did u get they -3 from?

- jdoe0001

x-3y=-3 <---
3x+y=1

- jagr2713

is this correct
(0,3) (-9,0)
and
(0,3) (2,0) ?

- jdoe0001

hmmm 0, 3 is not, -9,0 isn't either

- jdoe0001

x =0
x -3y=-3
0-3y=-3
y = (-3)/(-3)
y =1

- jagr2713

x-3y=-9
-3y=-9
y=1/3
x-3y=-9
x=-9

- jdoe0001

x=-9
(-9)-3y=-3
-3y=-3+9
-3y=+6
y=(6)/(-3)
y=-2

- jagr2713

wait this is confusing me
dont u put 0 for them?

- jdoe0001

wel... you said it was
x-3y=-3
3x+y=1
but now you seem to have changed it some

- jagr2713

OHOHOHO I've been doing the wrong problem... :D KML

- jagr2713

I WAS LOOKING AT THE QUESTION LOL

- jagr2713

i got
(0,1) (-3,0)
and
(0,1) (3,0)

- jdoe0001

but all you need to graph a line is
two points
\(\begin{array}{llll}
x-3y=-3\implies \cfrac{x+9}{3}={\color{brown}{ y}}\\
6x+y=3\implies {\color{brown}{ y}}=3-6x
\end{array}\)
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIoeCs5KS8zIiwiY29sb3IiOiIjM0IxRENGIn0seyJ0eXBlIjowLCJlcSI6IjMtNngiLCJjb2xvciI6IiNENDExMTEifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItNi41NCIsIjYuNDYiLCItMi40OCIsIjUuNTIiXX1d

- jagr2713

D: it says my answer is wrong...
i did the x|y thing

- jdoe0001

check yours PEMDAS I'd think

- freckles

I'm confused... Are you saying you got 3 different solutions for
x-3y=-3
3x+y=1 ?
You should only get one solution, infinitely many solutions, or no solutions for system of linear equations.

- jagr2713

OHH my friend told me to use y=mx+b

- freckles

why?
aren't you trying to solve the system
x-3y=-3
3x+y=1
?
or is that not the question?

- jagr2713

yes by graphing it thou but i did it and getting it wrong D:

- freckles

you should just get a point for the solution of this system:
you will see that when graphing these two lines that they will share a common point
that point is the solution
x-3y=-3
-3y=-x-3
y=1/3*x+1
---
3x+y=1
y=-3x+1
so graphing both y=1/3*x+1 and -3x+1
we have something that looks like this:
|dw:1442275696567:dw|
the solution is given at the point where both lines touch each other (cross each other; intersect each other)

- freckles

|dw:1442275792808:dw|
so this point I darkened is the solution
because is the point that two lines have in common

- jagr2713

wait can u try thing one
x-2y=-2
4x+y=1

- freckles

were you trying to write in y=mx+b form to graph the lines to find the point ?

- jagr2713

yea i was using that

- freckles

ok well try writing x-2y=-2 in that form

- jagr2713

2y=x+2 right?

- freckles

so you subtracted x on both sides and multiplied -1 on both sides?
x-2y=-2
subtracted x on both sides
-2y=-x-2
multiplied both sides by -1
2y=x+2
this is correct so far
then just divide both sides by 2

- jagr2713

yea i got
y=1/2x+1

- jagr2713

then u graph it by going to (0,1) then rise over run

- freckles

that sounds great
so y=1/2x+1 says the y-intercept is 1 and the slope is 1/2
|dw:1442276083294:dw|
right so you get something like this
now we also need to graph 4x+y=1 on that same graph

- freckles

4x+y=1
is equivalent to
y=-4x+1
can you try graph that
we should actually already see the solution even before graphing

- jagr2713

yea
we got 0,1 then rise over run -4/1

- freckles

so before graphing you should see that (0,1) is a point on both graphs where both graphs differ in slope therefore (0,1) is the solution

- jagr2713

yea 0,1 is the slope so we go down 4 and move 1 to the left right?

- freckles

(0,1) is the y-intercept
the slope is -4/1 so we move down from the y-intercept 4 units and to the right once

- jagr2713

Oh right 1 sorry my friend told me left....

- jagr2713

OMG your the best :D

- jagr2713

can u help with one more but this one is substitution

- freckles

sure

- freckles

one more then I have to roll my croissant dough

- jagr2713

ok :D
4x+y=24
y=2x

- freckles

replace first y with (2x)
solve 4x+2x=24 for x

- jagr2713

don't you reverse it like y=4x+24 and plug into x
y=2(4x+24)

- freckles

the second equation says y=2x
so you insert that y here: 4x+y=24 to get 4x+2x=24
anyways you can't replace x with 4x+24 because we aren't given x=4x+24
unless you already know that x=-8 which x doesn't -8
and also 4x+y=24 is not equivalent to y=4x+24

- jagr2713

wait how did u get 4x+2x=24

- freckles

\[\color{red}{y=2x} \\ 4x+\color{red}{y}=24 \\ \\ 4x+\color{red}{2x}=24\]

- freckles

I replaced y with 2x because one of the equations said y=2x

- jagr2713

Wait i understand igtg thanks for the help

- freckles

k peace

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