Question

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?

Answer 1

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

Answer 2

Yes.

Answer 3

Okay, gimme a sec. (writing problems down)

Answer 4

Sure.

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

How did you get 1.2x?

Answer 11

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

Answer 12

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

Answer 13

Do you remember the additive identity property?

Answer 14

Yeah.

Answer 15

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

Answer 16

That's how I was able to rearrange the terms

Answer 17

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

Answer 18

I know that part to.

Answer 19

Okay

Answer 20

So did you arrange the like terms correctly?

Answer 21

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

Answer 22

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

Answer 23

That's what I see.

Answer 24

Okay.

Answer 25

Standard form is X + Y = Z

Answer 26

Your going to solve for one variable right?

Answer 27

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

Answer 28

I thought standad form was Ax + By = c?

Answer 29

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

Answer 30

It's cool.

Answer 31

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

Answer 32

Okay and then your going to add it?

Answer 33

I got 3x = - 19

Answer 34

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

Answer 35

Okay.

Answer 36

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)

Answer 37

Would you add them together please?

Answer 38

3x = - 45

Answer 39

x = -15

Answer 40

Yup! Now you just need to clean up.

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

Hey I checked..and your right.

Answer 48

The solution is (-15, -62)

Answer 49

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

Answer 50

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

Answer 51

It's cool.

Answer 52

Thanks.

Answer 53

Anyway, awesome. Take it easy, and God bless with the rest of your homework.

... Yikes. I think I need some sleep!

Answer 54

Lol. Me too.