OK. I need help solving a linear system by using the elimination method, but I also need to arrange the like terms, but sadly I don't know how. The linear system is 1. 2x - y = 32 2. y -5x = 13. The second equation needs to be arranged. Please help?

- anonymous

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- schrodinger

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- anonymous

I'll try to help. Are you still around?

- anonymous

Yes.

- anonymous

Okay, gimme a sec. (writing problems down)

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## More answers

- anonymous

Sure.

- anonymous

The first trick, is to line the equations up, with all of the variables and numbers in columns. This makes it easier to see what we're looking at.

- anonymous

Yeah I did that. I need to write it in standard form, but the x and y are in the different places.

- anonymous

So, in other words, here is how I rewrote them.
-y + 1.2x = 32.2
y - 5x = 13

- anonymous

Oh, lol, I didn't even think about standard form.

- anonymous

The original equation for the first one is 2x - y = 32

- anonymous

How did you get 1.2x?

- anonymous

Ahhhh! Okay. Let's rewrite the equations in standard form. ( I read your first post wrong)

- anonymous

2x - y = 32
5x - y = 13

- anonymous

Do you remember the additive identity property?

- anonymous

Yeah.

- anonymous

Okay. That property lets us move the addition/subtraction terms around however we like.

- anonymous

That's how I was able to rearrange the terms

- anonymous

Do you also remember that you can multiply both sides by a negative?

- anonymous

I know that part to.

- anonymous

Okay

- anonymous

So did you arrange the like terms correctly?

- anonymous

2x - y = 32 5x - y = 13 ?

- anonymous

I'm going to multiply the top equation by negative one, and then I'm going to add the two equations together. And, yes.

- anonymous

That's what I see.

- anonymous

Okay.

- anonymous

Standard form is X + Y = Z

- anonymous

Your going to solve for one variable right?

- anonymous

Yup. One way we can accomplish this is by adding the two equations together.

- anonymous

I thought standad form was Ax + By = c?

- anonymous

Uhh.. Yes. You're more right. (Sorry, haven't used standard form in a while)

- anonymous

It's cool.

- anonymous

Okay. So let's multiply by (-1)
2x - y = 32 becomes
-2x + y = -32

- anonymous

Okay and then your going to add it?

- anonymous

I got 3x = - 19

- anonymous

Yes! Now, it becomes very apparent why adding equations is awesome.
-2x + y = - 32
+ 5x - y = 13 ( I need to double check the negatives)

- anonymous

Okay.

- anonymous

Yeah, it's
-2x + y = -32
+ 5x - y = -13
I didn't need to multiply the top equation by negative one, (oops!), so I multiplied the bottom one, so that they'll add up nicely again. (Sorry for the confusion)

- anonymous

Would you add them together please?

- anonymous

3x = - 45

- anonymous

x = -15

- anonymous

Yup! Now you just need to clean up.

- anonymous

Now, substitute x for - 15 on another equation, and you'll get y. ^^

- anonymous

-2(-15) + y = -32 30 + y = -32 y = -2

- anonymous

Hmm..... Something went wrong. Argh! Sorry!!

- anonymous

I use it in the original equation don't I?

- anonymous

Alright, let's try this one more time! Hang on, gimme a second.

- anonymous

2(-15) - y = 32 -30 - y = 32 -y = 62 y = -62

- anonymous

Hey I checked..and your right.

- anonymous

The solution is (-15, -62)

- anonymous

O_O Yeah. I checked it. Just some bad 'rithmatic

- anonymous

Ow. Okay, cool. Whew. I was worried I led you down the wrong path. Hehe

- anonymous

It's cool.

- anonymous

Thanks.

- anonymous

Anyway, awesome. Take it easy, and God bless with the rest of your homework.
... Yikes. I think I need some sleep!

- anonymous

Lol. Me too.

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