Question

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

Answer 1

6
-3
3
-6

Answer 2

@qweqwe123123123123111 do u know the answer?

Answer 3

I'm playing with it... :-)

Answer 4

okay :)

Answer 5

Okay...ya there?

Answer 6

ya

Answer 7

Okay. So let's take one of your expressions and figure out an xy equivalency:
3x + 2y = 6

first, let's isolate the Y term by subtracting 3x from both sides. Can you do that?

Answer 8

subtracting it from 3 and 6?

Answer 9

No, just the entire 3x term. Subtract it from both sides of the "=" sign.

Answer 10

1y=6?

Answer 11

No...let me try showing what I mean this way:
To subtract 3x from both sides of
3x + 2y = 6
you do this:
3x - 3x + 2y = 6 - 3x

Answer 12

2y=3x

Answer 13

Almost...

subtracting the 3x from the left side did leave you with 2y.
But subtracting it from the right side doesn't get rid of the 6

Answer 14

6-3x can u help me with that i dont get how the 6 isnt gone

Answer 15

Okay, we have to work on both sides of the equal sign.
We do that because the left side is equal to the right side.
So if we have 3x+2y on the left side, and 6 on the right side, then we want to move the 3x from the left side to the ride side so that we can figure out what "Y" is equal to.

So 3x+2y-3x is the same as 3x-3x+2y
3x-3x = 0, so all we have left is 2x

but we also have to subtract 3x from the right side, too.
The right side is "6", so if we subtract 3x from 6, we have 6-3x

So we started out with
3x + 2y = 6
And we subtracted 3x from both sides and ended up with
2y = 6 - 3x

Do you see how that works?

Answer 16

yea so 2y=6-3x

Answer 17

Right!

So now we can DIVIDE both sides by 2. We have to do this because then we'll have an equation that says "Y = " whatever it's equal to. This is part of "solving for Y".

So can you divide all the elements on both sides by 2?

Answer 18

y=3?

Answer 19

No, 2y/2 = y

We also need to know what 6/2 is, and what 3x/2 is

Answer 20

6/2 is 3 and 3x/2 1.5

Answer 21

Almost.

6/2 is 3
and
3x/2 =1.5x

so dividing
2y = 6 - 3x
by 2 is:
y = 3 - 1.5x

And so now we no what Y is equal to, right?

Answer 22

1.45?

Answer 23

*And so now we KNOW what Y is equal to, right?

Stupid keyboard... :(

Answer 24

it cant be 1.45 like i think because thats not an option

Answer 25

No.

Right now, all we have is an equivalency, the equation can't be solved numerically.

What we know is that Y = "3-1.5x", so we can use that to replace "Y" in the second equation:
2x + 3y = -6
This is where we can figure out exactly what the value of "X" is.
We do this by replacing all the "Y"s with "3-1.5x"

So now:
2x + 3y = -6
is seen as:
2x + 3(y) = -6
and becomes
2x + 3(3-1.5x) = -6

rewrite 3(3-1.5x) as 3*3 - 3*1.5x = 9-1.5x

This gives you:
2x + 9 - 1.5x = -6

Can you see that?

Answer 26

oooooooo yea so its -6 thank you alot :)

Answer 27

Well, yes it is.

But we didn't solve for it, you just got lucky. To add insult to injury, I made a typo
2x + 9 - 1.5x = -6
should be
2x + 9 - 4.5x = -6

To finish off (since you probably answered already and got it right), taking:
2x + 9 - 4.5x = -6
we want to put the numbers on one side and the variables on the other, so we should subtract 9 from both sides like this:
2x - 4.5x = -6 - 9
Combining terms gives you:
-2.5x = -15
Dividing both sides by -2.5 yields:
x = 6

This is our first absolute value.

Now we can replace all the "X"s with "6":
2x + 3y = -6
becomes
2*6 + 3y = -6
12 + 3y = -6
subtracting 12 from both sides gives
3y = -6 -12
which is:
3y = -18
Dividing both sides by 3 yields:
y = -6

So you see that the answer IS -6, but it wasn't actually figured out until this last step.