Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
4x-8y=48
11x+3y=-105.5

- anonymous

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- campbell_st

simplify 4x - 8y = 48 to x - 2y = 12 (1) and 11x + 3y = -105.5 (2)
then use (1) x 11 - (2) which will eliminate x and solve for y

- anonymous

yikes another one with decimals!

- anonymous

you got this?

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## More answers

- anonymous

no not really

- anonymous

hold on we can do it

- anonymous

\[x - 2y = 12 \]
\[11x+3y=-105.5\]

- anonymous

multiply the first equation by -11 and add to the second one

- anonymous

ok is it 2y or 3y

- anonymous

\[-11x+22y=132\]
\[11x+3y=-105.5\]

- anonymous

is it suppose to be x-2y or x-3y?

- anonymous

first equation simplifies by dividing by 4, giving you
\[x-2y=12\]

- anonymous

oh ok

- anonymous

now add the two equations together

- anonymous

the x terms add up to zero and you get
\[25y=26.5\] if my arithmetic is correct

- anonymous

damn i screwed up again!

- anonymous

ok lol we can fix it

- anonymous

you multiply the first one by -11

- anonymous

\[-11x+22y=-132\]

- anonymous

i forgot the negative on the right hand side

- anonymous

ok so where does that come in

- anonymous

\[-11x+22y=-132\]
\[11x+3y=-105.5\]

- anonymous

ok lets go slow

- anonymous

you have
\[x-2y=12\]
\[11x+3y=-105.5\] right?

- anonymous

ok

- anonymous

and you want to eliminate one of the variables so you can solve on equation with one variable

- anonymous

i am confused on what comes first can you lay it out the way it suppose to be

- anonymous

yes it looks like this

- anonymous

ok

- anonymous

\[x-2y=12\]
\[11x+3y=-105.5\]
then
\[(-11)\times (x-2y)=(-11)\times 12\]
\[11x+3y=-105.5\]
then
\[-11x+22y=-132\]
\[11x+3y=-105.5\]

- anonymous

you have to figure out for yourself that if you multiply the first equation across by -11 and then add, the x terms will drop out when you add the two equations. finding what to multiply by is up to you.

- anonymous

i am lost

- anonymous

now add and get
\[25y=-235.5\] so now
\[x=-237.5\div 25=-9.5\]

- anonymous

why don't we try an easy one first. suppose i see
\[x+y=1\]
\[x-y=7\]how can i find x and y?

- anonymous

if you add the two equations together you get
\[2x=8\] because you get
\[x+y+x-y=1+7\]
\[2x=8\]

- anonymous

ok

- anonymous

now i have one variable and one equation, so easy to solve, if
\[2x=8\] then
\[x=4\] and if i know
\[x=4\] then i know
\[y=3\] because the first equation says
\[x+y=7\] so
\[4+y=7\] and therefore
\[y=3\]

- anonymous

unfortunately in your problem if i simply add, nothing drops out. so you have to arrange it so that one of the variables will go away when you add

- anonymous

ok when it comes to my problem i get really lost

- anonymous

so for example if i see
\[2x+3y=7\]
\[x-y=1\] have to get rid of one variable by multiplying one equation all the way across by a number that will make one of the variables go away when i add

- anonymous

so i could multiply the second equation by 3 and get
\[2x+3y=7\]
\[3x-3y=3\] and now it is easy add to get
\[5x=10\] so
\[x=2\]

- anonymous

in your problem you have
\[x-2y=12\]
\[11x+3y=-105.5\]

- anonymous

to make one of the variables go, multiply the top one by -11 so you will have
\[-11x\] in the first equation and
\[11x\] in the second one, and they will add up to zero

- anonymous

we have to multiply EVERYTHING by -11 in the first equation and we get
\[-11x+22y=-132\]
\[11x+3y=-105.5\]

- anonymous

now when you add there will be no more x's

- anonymous

ok is that the first part or the second part

- anonymous

i am not sure what you mean

- anonymous

step one was to turn
\[4x-8y=48\] into
\[x-2y=4\]

- anonymous

step two was to multiply by -11 to get
\[-11x+22y=-132\]

- anonymous

step 3 is to add it to the second equation. the x's add to zero and you get
\[25y=-137.5\]

- anonymous

step 4 is to solve for y via
\[y=-237.5\div 25\]
\[y=-9.5\]

- anonymous

typo in step 3, should have been
\[25y=-237.5\]

- anonymous

and finally to find x, replace y by -9.5 in either equation

- anonymous

ok with x would you divide by 2 for the first step as well

- anonymous

\[x-2y=12\]
\[x-2\times (-9.5)=12\]
\[x+19=12\]
\[x=12-19\]
\[x=-7\]

- anonymous

you can divide the first equation by 4, because each term has a common factor of 4
just makes it easier to work with

- anonymous

in general no, you do not divide as a first step. in general you see what you can multiply one equation by to make one variable drop out when you add the two equations

- anonymous

ok still a little lost but getting the hang of it

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