Question

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

Answer 1

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

Answer 2

yikes another one with decimals!

Answer 3

you got this?

Answer 4

no not really

Answer 5

hold on we can do it

Answer 6

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

Answer 7

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

Answer 8

ok is it 2y or 3y

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

oh ok

Answer 13

now add the two equations together

Answer 14

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

Answer 15

damn i screwed up again!

Answer 16

ok lol we can fix it

Answer 17

you multiply the first one by -11

Answer 18

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

Answer 19

i forgot the negative on the right hand side

Answer 20

ok so where does that come in

Answer 21

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

Answer 22

ok lets go slow

Answer 23

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

Answer 24

ok

Answer 25

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

Answer 26

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

Answer 27

yes it looks like this

Answer 28

ok

Answer 29

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



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

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

Answer 30

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.

Answer 31

i am lost

Answer 32

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

Answer 33

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?

Answer 34

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

Answer 35

ok

Answer 36

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
\[y=3\]

Answer 37

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

Answer 38

ok when it comes to my problem i get really lost

Answer 39

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

Answer 40

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
\[x=2\]

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

ok is that the first part or the second part

Answer 46

i am not sure what you mean

Answer 47

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

Answer 48

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

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

ok still a little lost but getting the hang of it