lol

- anonymous

lol

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- anonymous

add both equations

- anonymous

you'll get 2x = 22

- anonymous

solve for that, and you'll get 11

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## More answers

- anonymous

I though that too, but that's not an answer. :(

- anonymous

thought*

- anonymous

what are the options?

- anonymous

-22
-12
-2

- anonymous

I have to go, I'll respond to this in a little bit. Sorry.

- tkhunny

x + y = 12
x - y = 10
D = (1)(-1)-(1)(1)
Dx = (12)(-1)-(10)(1)
Dy = (1)(10)-(1)(12)

- anonymous

That's fine. Thanks though :)

- anonymous

Are you saying it's -22? It's asking for the x determinant if you're wondering. I just want to be able to solve the future ones. :)

- mathmale

@ambeeeerlw : Determinants are not used much any longer. However, you're apparently expected to know how to apply determinants to solving systems of linear equations. Have you tried looking up "determinants" on the 'Net? If you want to learn how do use determinants, either @tkhunny or I would be happy to help you ... but we do not give out just answers.

- anonymous

I actually wasn't expecting just answers, I was double checking his work so I'd know how to future problems. I'm not trying to just collect answers, I swear. I have looked it up, but I can;t a way that explains it well enough where I fully understand. :( Can you help me?

- anonymous

( or her work, I didn't see who it was)

- tkhunny

"Cramer's Rule" is very interesting. It just works. It leans toward what we like to call an "Existence" result. This means it may or may not be very useful in the real world, but it demonstrates that (or under what conditions) the solution exists. Good thing to know.

- anonymous

My teacher didn't even mention it is "Cramer's Rule," so that's a nice factor to know.. I do online school, and I can't really get it touch with my teacher, reasoning behind me getting help from her.

- mathmale

@tkhunny typed this out for you earlier:
x + y = 12
x - y = 10
D = (1)(-1)-(1)(1)
Dx = (12)(-1)-(10)(1)
Dy = (1)(10)-(1)(12)
First, he found the "system determinant." He realized that
x + y = 12
x - y = 10
can be re-written as 1x+1y=12
1x-1y=10
which we need to do because we need those coefficients of x and y.
Notice how the coefficients (alone) are 1 1
1 -1
tkhunny now finds the "system determinant."|dw:1396529907980:dw|

- mathmale

The result is -1 -1, or -2. The system determinant is -2. Note that this is exactly the result obtained by tkhunny earlier. Have you seen this kind of work done before?

- anonymous

Yes, that is the only one have and that I understand.

- mathmale

Good. Now we need to find x. We take the system determinant, toss out the first column, and replace it with the constants (12 and 10):|dw:1396530274277:dw|

- anonymous

the products of those would be -12 and -10, right?

- mathmale

Right, and that adds up to -22.
Thus, your x is found in this manner:|dw:1396530623039:dw|

- anonymous

10?

- mathmale

close. Try again.

- mathmale

and your y value is

- anonymous

I meant 11, oops :p

- anonymous

y value is 1? I think

- mathmale

|dw:1396530712310:dw|

- mathmale

Cool. Yes, y=1. Solution is (11,1). congrats!

- anonymous

I don't understand because the answers are only -22,-12, and -2. This is what confuses me

- anonymous

Is it asking for another part of the question? I'm unsure.

- mathmale

@tkhunny's "answers" are intermediate results.
He gave you D=-2, Dx = -22 and Dy = -2.|dw:1396531164233:dw|

- mathmale

that's right!! they are both modifications of the system determinant.

- mathmale

And nothing to apologize for! I so much appreciate your sticking with this until completion. Hope to get to work with you again.

- mathmale

That's like music to the ears! :)

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