How to solve systems with elimination?
5x - 2y = 28
-20x + 8y = -100
I know that if there are two of the same variable then they cancel and then it is easy to solve when you add the equations together, but what if neither equation has corresponding variables???

- icalibear

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- anonymous

you have to make them become corresponding
5x-2y= 28 (multiply by 8 ) = 80x-16y =224

- icalibear

How are those corresponding :s

- anonymous

and you have to make this for the second one
-20x +8y=-100 (muliply by 2) = -40x +16y = -200
and solve by elimination now

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## More answers

- anonymous

eliminate 16y

- icalibear

why did you multoply by 8 and 2 sorry

- UsukiDoll

If I was given that problem I would eliminate x... seems easier if I distribute the 4 all over the first equation

- UsukiDoll

and for that reason. I have to distribute the 4 all over the first equation because I want to eliminate a variable and solve for the other. In this case,
4(5x-2y=28)
20x-8y=112 (this is my new first equation)
so I add my new first equation to the second equation so I can get rid of the x

- anonymous

to make them corresponding...

- anonymous

@Michele_Laino please help

- icalibear

i got 3/5...

- UsukiDoll

oh geez we are forced to take the y's out and then solve for x
because by distributing the 4 all over the first equation, I ended up destroying x and y., and we don't want that.

- UsukiDoll

\[8(5x-2y=28)\]
\[2(-20x+8y=-100)\]
\[40x-16y=224\]
\[-40x+16y=-200\]
HUH? Am I reading this wrong? even I got the same problem.

- anonymous

i was right @icalibear

- icalibear

|dw:1434862139806:dw|

- icalibear

i meant to type 40x

- icalibear

sorry! typo

- icalibear

i will fix this

- UsukiDoll

we are supposed to distribute 8 and 2 THROUGHOUT THE equation. We can't have it one sided

- icalibear

|dw:1434862362988:dw|

- UsukiDoll

your x portion is off and when you fix it... x and y will cancel

- anonymous

i made a mistake on the multiplication.. sorry

- hartnn

40x - 40x = 0
-16y +16y = 0
224 -200 =24
so you get
0 = 24 in the end.
Is that even possible?

- icalibear

is there even a solution if both x and y cancel because that leaves nothing

- UsukiDoll

it's an inconsistent system which leads to no solutions at all

- hartnn

0 =24
true or false?

- icalibear

false..

- icalibear

so there is no solution

- hartnn

right, so there is NO value of x or y which can satisfy those 2 equations.
correct, no solution!

- icalibear

okay

- icalibear

thanks so much guys.. i do not remember this from 9th grade..

- UsukiDoll

yeah. I did it both ways... when I tried to eliminate x and I ended up with x and y going away
similarly when I tried to eliminate y, I ended up and x and y going away as well
leaving me
with both situations having
LHS doesn't equal the RHS
left hand side doesn't equation the right hand side.

- icalibear

okay

- UsukiDoll

but I still would've done the x first... multiply that first equation by 4 makes it faster to get to the conclusion

- UsukiDoll

\[4(5x-2y=28)\]
\[-20x+8y=-100\]
\[20x-8y=112\]
\[-20x+8y=-100\]
adding these two equations forces x and y to disappear.

- icalibear

I have one more..

- icalibear

I multiplied to get the middle terms the same but then i got a fraction

- icalibear

Nevermind made an error
! 6 x 3 is 18

- icalibear

|dw:1434862940828:dw|

- icalibear

is this set up right

- hartnn

yes!

- UsukiDoll

yes it is.

- icalibear

so x = 9

- hartnn

yup

- icalibear

okay

- hartnn

y =.. ?

- UsukiDoll

yay... that was fast x)

- hartnn

yes, she got it, she is now unstoppable! ;)

- UsukiDoll

:D

- icalibear

I didnt need to find y for the question but i know you would substitute it back in

- icalibear

thanks so much guys :)

- hartnn

right, go ahead and find it...you're doing it to learn, right?
not just for completing the homework...

- icalibear

yes this is just practice

- UsukiDoll

practice is fine....it's the questions with so many questions and multiple choices with omg this is due in an hour are frown upon on os

- icalibear

this isnt a class i get credit for, its just summer prep so i can get into math 128 in the fall

- icalibear

ive graduated and I forgot every bit of this intermediate algebra!

- UsukiDoll

actually... well in my textbook... this is elementary algebra 1

- icalibear

either way, I need a refresher

- hartnn

waiting for the y value :P

- icalibear

sorry i have moved way on.. D:

- hartnn

its ok ^_^
probably next time :)

- icalibear

Yep

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