Question

solve this by elimination method x/2+y/5=14/15 and x/3-y/12=2/3 with complete solution please.tnx

Answer 1

\[\frac{x}{2}+\frac{y}{5}=\frac{14}{15}\]
\[\frac{x}{3}-\frac{y}{12}=\frac{2}{3}\]

Answer 2

working on it now.

Answer 3

hating fractions, i would multiply everything by 60 before i started messing around
\[15x+15y=28\]
\[20x-5y=40\] now at least i can see what i am doing

Answer 4

wait 73
x/2 * 60 = 30x

Answer 5

looks like multiply second equation by 3 will do it
\[30x+15y=56\]
\[60x-15y=120\]

Answer 6

yeah i messed up top one twice actually. it is early. think it s right now yes?

Answer 7

top one is right.

Answer 8

\[60\times \frac{14}{15}=14\times 4=56\] i think that line is now correct yes?

Answer 9

got it from here?

Answer 10

that is correct., and for bot i just multpied x/3 and 2/3 by 4. so i got
4x - y = 12

Answer 11

wait i find the LCD THE LCD OF FIRST IS 10 AND THE OTHER 1 IS 12 but i do't know what is the next step

Answer 12

wait wait, i made an error, its 4x - y = 8

Answer 13

i had the probably unnecessary large equations
\[30x+15y=56\]
\[20x-5y=40\]

Answer 14

yup so i made it
30x +15y = 56
60x -15 = 120

Answer 15

then say multiply second equation by 3 so you will have 15y and -15y which will add to get 0

Answer 16

-15y

Answer 17

@daverer is that step clear? you want to "eliminate" one of the variables

Answer 18

176/90 = x
x = 1.96

Answer 19

correct?

Answer 20

actually
\[x=\frac{176}{90}=\frac{88}{45}=1.9\overline 5\]

Answer 21

then i sub in for x, and i got y = -0.178

Answer 22

but rounded you get what you wrote

Answer 23

this problem is a pain

Answer 24

and thats rounding its 1.777777

Answer 25

how do you write it mathematically?

Answer 26

hold on. may be some mistake here. let me see if i can find it

Answer 27

... this problem is really a headache ...... this is our new lesson and it's hard.

Answer 28

just tried machine and got different answer so i will go slow
first equation is
\[\frac{x}{2}+\frac{y}{5}=\frac{14}{15}\] multiply by 60 to get
\[30x+12y=56\] oh heavens i messed this all up. should be
\[30x+12y=56\] now what i wrote earlier.

Answer 29

i wrote it as y/4
that was my fault :(

Answer 30

ok now we can continue. second equation is
\[\frac{x}{3}-\frac{y}{12}=\frac{2}{3}\] multiply by 60 to get
\[20x-5y=40\]

Answer 31

now at this point i would use substitution rather than elimination because second equation is
\[4x-y=8\]
so you could put
\[y=4x-8\] and solve

Answer 32

were do you multiply it anyway?

Answer 33

sure lets finish this up. first equation is
\[15x+6y=28\] second is
\[4x-y=8\]

Answer 34

multiply second by 6 to get
\[15x+6y=28\]
\[24x-6y=48\]

Answer 35

add the two equations to get
\[39x=76\]

Answer 36

and finally
\[x=\frac{76}{39}\] a painful but correct answer

Answer 37

oh.oh it's really hard for me

Answer 38

yes well this was an annoying one. especially since we got off to a false start. steps were these
a) multiply first equation by 15
b) multiply second equation by 12

this clears the fractions
c) multiply second equation by 6 so the y's will drop out when you add
d) add

now you have one equation in one variable. solve

e) substitute back to see what the other variable is

Answer 39

correct answer is
\[x=\frac{76}{39},y=-\frac{8}{39}\]

Answer 40

do you know how to check this? checking..

Answer 41

yes put the numbers x and y into the other equation as well to see if you get the correct equation.