Question

What is the value of the y variable in the solution to the following system of equations?
3x + 2y = 6
2x + 3y = −6

A: 6

B: −3

C: 3

D: −6

*i got -3 but i want to make sure im right.

Answer 1

it might be right, how did you obtain it?

Answer 2

i dont get a -3

Answer 3

2(3x+2y)=2(6)
3(2x+3y)=3(-6)

Answer 4

well i did it some weird way , like my own way so thats why i wasn't sure if it was right

Answer 5

if we know the way you tried it, we can hone it better

Answer 6

6x + 4y = 12?
6x + 9y = -18?
@jiteshmeghwal9

Answer 7

i have make one of the variable equal to gt the value of 'y' :)

Answer 8

equal but opposite is another strategy that eliminates an extra step out of that

Answer 9

i deleted my reply before u see

Answer 10

okay wait can you explain it to me again?

Answer 11

lol ;)

Answer 12

im soo confused....

Answer 13

it would be better to work off of the method you tried on your own .. imo

Answer 14

cool down friend amistre is here .. be happy and enjoy the learning @Rkb<3NH

Answer 15

yea but i got 6x = 2 at the end

Answer 16

im not concerned with the endl id like to see the process you did to correct it

Answer 17

ok
wait

Answer 18

3x + 2y = 6
-3x -3x
2y = 6 - 3x
2x + 3y = −6
2x +(6-3X) 3y = −6
12x - 6x + 3y = -6
6x + 3y = -6
/ 3 /3
6x = 2??

Answer 19

so your trying to do substitution

Answer 20

yea i tried elimation but to me it dident work out

Answer 21

you should start out by solving for an "x" to find the "y"

in order to replace the "x"; we substitute it with its y equivalent

does that make sense?

Answer 22

3x + 2y = 6
-2y -2y
-----------
3x = 6-2y

x = (6-2y)/3

Answer 23

yes but why did you divide by 3?

Answer 24

because 3x does not equal x

Answer 25

3x/3 = x

Answer 26

3x = 6-2y
/3 /3
------------
x = (6-2y)/3

Answer 27

so i will be
2x + (6 -2y)/3 +3y = -6
12x + 4y/3 + 3y = -6
is that good so far?

Answer 28

4x +4/3y +3y = -6
i went wrong here, i dont knw

Answer 29

what to do

Answer 30

almost; lets clarify this "substitution"

given that: x = (6-2y)/3

and 2x + 3y = -6

REPLACE (substitute) the equation of "x" in place of "x"

\[2x + 3y = -6\]
\[2\frac{(6-2y)}{3} + 3y = -6\] ^^^
we replaced "x"

Answer 31

12x - 4y/3 + 3y = -6
isn't that what i jut got because i cant divide 4/3

Answer 32

there shouldnt be any "x" left to play with in this equation

Answer 33

(12 - 4y)/3 + 3y = -6

Answer 34

4y - 4/3y + 3y = -6?

Answer 35

lets work this slowly

(12 - 4y)/3 + 3y = -6\[\frac{12 - 4y}{3} + 3y = -6\]\[\frac{12}{3} - \frac{4y}{3} + 3y = -6\]\[4 - \frac{4}{3}y + 3y = -6\]-4 -4
-----------------\[- \frac{4}{3}y + 3y = -10\]
good so far?

Answer 36

6x+4y=12
6x=12+4y
x=12+4y/6

Answer 37

@jiteshmeghwal9 just a request to you :

let amistre64 finish his explanation to the user .. please

Answer 38

k!

Answer 39

yes

Answer 40

and jite, your mathing;

6x+4y=12
6x 12+4y ; is off a little

just saying :)

Answer 41

but 4/3y + 3y is 4.33333333...

Answer 42

Rkb, good. as long as its making sense to far, lets continue; without worrying about turning fractions into decimals ....
\[- \frac{4}{3}y + 3y = -10\]
\[\left(3-\frac{4}{3}\right)y = -10\]
\[\left(\frac{9}{3}-\frac{4}{3}\right)y = -10\]
\[\frac{5}{3}y = -10\]

still good?

Answer 43

ok i get it now so it will be
3 * 5/3 = -10 * 3
5 = 30?
good so far?

Answer 44

thats pretty good, dont forget the negative from that 10 tho

3 * 5/3 y = -10 * 3
5y = -30

Answer 45

oh okay:
y = -6!!??(:

Answer 46

correct :) y = -6

Answer 47

cool math @amistre64 :)

Answer 48

thanx; elimination is quicker if you can work your head around it; but subbing is just as fine if your more comfortable with it

Answer 49

yes! i was going through elimination method ut @mathslover saide to me that we should see ur explanation first :)

Answer 50

thank you soo much @amistre64 (:
And thank you tooo @jiteshmeghwal9 (:
im glad you didn't just give me the answer you you helped me out(:

Answer 51

3x + 2y = 6
2x + 3y = −6

3x + 2y = 6 ; *2
2x + 3y = −6 ; *-3

6x + 4y = 12
-6x -9y = 18 ; combine them
--------------
-5y = 30
/-5 /-5
-----------
y = -6

Answer 52

\[\Huge{\color{red}{you \space are \space welcome :) }}\]