Question

PLEASE HELP!!!
1/2 x + 1/3 y = 7 and 1/4 x + 2/3 y = 6
Y = 5, X = 10 2/3
Why?

Answer 1

hi. thanks for coming over to help =)

Answer 2

so first....turn them into slope intercept form...that is....isolate y

Answer 3

ok...working that on paper right now...

Answer 4

(1/2x + 1/3y = 7)3...1 1/2x + y = 21...y = 21 - 1 1/2 x...correct?

Answer 5

(1/2x + 1/3y = 7)

FIRST isolate the y number....so subtract the 1/2 x from both sides...what do you have now?

Answer 6

you have 1/3y = 7 - 1/2x

Answer 7

correct...now...to isolate y ...how do we get rid of the 1/3? we multiply by 3 correct? so do that to both sides...now what do you have?

Answer 8

y = 21 - 3/2x ... so y = 21 - 1 1/2x

Answer 9

right...but keep it as an improper fraction...it's easier than a mixed number

but now for the next one

1/4 x + 2/3 y = 6

using the same process...what does this come out to?

Answer 10

solving for x this time?

Answer 11

No you're again isolating y...you'll see why in the next step after you find it

Answer 12

ok...doing right now...

Answer 13

1/4x + 2/3 y = 6...2/3y = 6 - 1/4x...y = (6 - 1/4x) 2/3...

Answer 14

* i mean times 3/2 at the end

Answer 15

then y = 18/2 -3/8x

Answer 16

correct.....just simplify totally...so y = 9 -3/8x

Answer 17

so now what 2 equations do you have?

Answer 18

i have y = 9 -3/8 and y = 21 - 3/2x

Answer 19

*-3/8x

Answer 20

so now i would combine them, correct?

Answer 21

right..the x after the -3/8x

so...now put them in proper form...y=mx+b......slope in front y intercept at the end

Answer 22

just rewrite them for clarity....

y = -3/8x + 9
y = -3/2x + 21

And yes...now combine them

Answer 23

that is...set them equal to each other

Answer 24

2y = 18/16 + 30

Answer 25

then i divide both sides by 2...

Answer 26

no no... i shouldnt have said combine them like i did.....that's why i corrected your statement....what do you do when y = 2 different things?

Answer 27

that's y = 9/8 + 15

Answer 28

say you have y = 2
and y= 3

that is the same thing as saying y = 2 AND 3 right?

in that same logic....that must mean 2 = 3

so in THIS tense....is y = both of those...set them equal to each other

Answer 29

that means that something is strange with the equation? like, if i were to graph it, it would be different shape than a line?

Answer 30

meaning

do it like this

-3/8x + 9 = -3/2x + 21

Answer 31

ok. now what?

Answer 32

now you can see that the only variable you have is x right?

that's what we're solving for.....so combine your x's and combine your constant numbers...then isolate x......what do you have?

Answer 33

but do you understand that logic behind setting the 2 equations equal to each other?

Answer 34

not exactly...but I did the equation: 26/16x = 18...right?

Answer 35

what is the least common denominator of -3/8x and -3/2x?

Answer 36

4

Answer 37

wait no- 8!

Answer 38

....correct with the 8......what do you need to multiply 2 by to get 8?

Answer 39

4

Answer 40

correct....so multiply 3/2 by 4/4

Answer 41

3/4

Answer 42

alright...lets lead up to what you've done so far

-3/8x + 9 = -3/2x + 21

subtract 9 from both sides

-3/8x = -3/2x + 12

now add -3/2x to both sides....

-3/8x + 3/2x = 12

this is where your least common denominator comes in..which is 8

(-3/8x) + (4/4) times 3/2x = 12

so

-3/8x + 12/8x = 12

Answer 43

combine those x's...what do we have?

Answer 44

alright i was just rereading what we did...9/8x = 12

Answer 45

perfect.....now how do you isolate x here?

Answer 46

multiply both sides by 8/9

Answer 47

correct...and what does that come to?

Answer 48

x = 96/9, or x = 10 and 6/9, which can be reduced to
x = 10 and 2/3

Answer 49

yay we did X =)

Answer 50

exactly! that's where your x comes from.....now for y....how would you find it? now that you have x?

Answer 51

I would substitute what x equalls and take an equation to find y...
1/2 (10 and 2/3) + 1/3 y = 7

Answer 52

that is correct

Answer 53

and so what do we get for y?

Answer 54

that would be 5 and 1/3 + 1/3y = 7...then 1/3y = 1 and 2/3...then...y = 3 and 1/2

Answer 55

that's not right....

Answer 56

Ahh i see what you did.....
so

1/2 x + 1/3 y = 7
1/2 (what we got for x) + 1/3 y = 7 ***turn the mixed number into an improper fraction

1/2(32/3) + 1/3 y = 7

so yes this is 5 and 1/3

7 - 5 and 1/3 IS 1 and 2/3

turn 1 and 2/3 into an improper fraction..what is that?

Answer 57

5/3

Answer 58

correct...so we have

1/3y = 5/3

how do we isolate y?

Answer 59

multiply by 3
y = 15/3...so...
y = 5
YAY!!!

Answer 60

haha...and that is your reasoning :)

Answer 61

thank you so much! i don't know what i'd do without open study and helpful people like you. have a great day! or evening...or whatever time it is on your side of the world... =)

Answer 62

lol you're welcome...glad to help!