Someone who knows some math please help me!
 

First off, lets get one thing straight. Im in a math calss that is way too hard for me. I shouldnt be in it, but I tested into it, so now im stuck in it. They are making us give an oral report of sorts on a math problem.(you would think they would cut us breakes from this ****, considering im in a smarter class, but no, we get to do fun projects like this ****.) So, normaly I would try to do this myself, but see, this is the problem. We sign up for a problem that was on our homework, and then the day we grade that homework assignment, is the day we do our reports. So my teacher wont explain the assignment(and how to do my problem) until the day before Im doing my report. And im going to be busy the night before my report, so wont have time to work on it then. Most people in my class allready know how to do these problems, so they dont have that problem, but im the dumbest one in my class, struggling to maintain a C- Average. So we have to explain the problem on the blackboard. So im going to give the problem I singed up for, and I want someone to plese explain how to get the answer, explaining the steps you took to get there. Im doing my report on Thursday. Here is the problem.

The Directions State:

Solve by either the substitution method or the addition-or-subtraction method.

My problem is:

x-5y=2
2x+y=4

the directions at the begining of the lesson tell you how to do it using the Addition method...this is how it says...

1. Add similar terms of the two equations.
2.Solve the resulting Equation
3. Substitute the number you get for x in either of the origional equations to find y.
4. Check in BOTH equations.

so you should end up with an ordered pair. I appreciate any help, although I probably wont get any. The most crucial thing is getting the correct answer, because if you dont, you get a zero.

Either multiply the bottom equation by 5 or the top equation by -2. Then add them.

Patheticly easily!!

x-5y=2
2x+y=4

x=2+5y

2(2+5y)+y=4
4+10y+y=4
11y=0
y=0

to find X

2x+y=4

substitute in for y

2x+0=4
2x=4
x=2

check for both equations

x-5y=2

2-5(0)=2
2=2 (first equation is true)


2x+y=4

2(2)+0=4
4=4

last equation is true



Now you better kiss my ass for waisting my time doing this.

Well, hopefully, Neo and azazela were helpful. If not, I'll explain this to you in as much excruciating detail as you can stand.

First off, I hope you understand algebraic addition, multiplication and a little bit on manipulating equations. Otherwise, you are truly screwed.

Okay, so your two equations are

x - 5y = 2
2x + y = 4

I am now going to explain what your directions mean.

A term is a variable (a letter) multiplied by a constant (a number). x and y are considered terms because they are actually multiplied by 1. Some people consider numbers by themselves to be terms, but don't worry too much about it.

Similar terms are terms with the same variable. So x and 2x are similar terms. -5y and y are terms. Note that I put the negative sign in front of -5y. In algebra, subtraction is considered to be the addition of a negative number rather than an operation all unto itself.

So to add the similar terms of the two equations, add the two terms with x together, add the two terms with y together and add the two numbers together. x + 2x = 3x, -5y + y = -4y, 2 + 4 = 6. Since all the variables are on the left of the equation and the constants are on the right of the equation, you can just stick all the variables in the same place. So using the results from that addition I just did, you'd get the equation 3x - 4y = 6.

What they mean is "solve the resulting equation for x" since the next instruction requires you to substitute a number for x. Unfortunately, this leads to some truly ugly fractions that I don't think you want to deal with (you'd get x = 2 + 4/3y). This is the other trick with solving by addition. You can multiply an entire equation by a constant. This is what Neo was talking about in his post. So let's say you choose to multiply the bottom equation by 5. Your system of equations is now

x - 5y = 2
10x + 5y = 20

Do you see how if you add those two equations, you'd eliminate y altogether? In other words, adding them gets you the equation

11x + 0y = 22

Which is the same thing as

11x = 22

I'm pretty certain you can figure out from here that x = 2 (if you're at least maintaining a C-, you can't be stupid enough to not understand how that works).

Ok, you just got a number for x. Namely, x = 2. So pick one of the equations and write it down, but every time you see an x, just write the number 2 instead. Remember, 2x means 2 multiplied by x. So if x = 2, then 2x is 2 times 2, not 22. I didn't think you would actually write 22, but I told you that I'd explain everything in excruciating detail.

Anyways, pick one of the equations and stick in 2 for x. Let's say you pick the top equation. The equation now becomes

2 - 5y = 2

You should be able to solve this, and for once, I'm not going to tell you what the answer is (even though azazela already did).

So that means whatever value you got for x, stick it into both equations, and whatever value you get for y, stick it into both equations. Then add everything up. If the numbers on both sides of the = sign are equal, then you've got the correct answer.

I can show you solving by substitution (which is a far superior method, in my opinion), but the directions didn't require you to know how to do that.

By the way, couldn't one of your parents have explained this to you?

*looks back over post*

Man, I have way too much time...

Well, there's nothing to add, except, yep, they both look right.

If you don't understand it just copy down what I wrote and come up to the teacher for exta help.

Wow, I remember those easy days of simple algebra (no offense Jason1). Just wait til calculus, which in it's self isn't too incredibly hard.

You think Cal is easy..You think Cal is EASY!!!!.. ARGH

This problem was nerve wrecking and annoying...

A tangent line drawn to the parabola y=4-x² at the pont (1,3) forms a right triangle with the coordinate axes. The area of the triangle is....

Here's how I do it.

Step 1: Buy a TI-89 calculator
Step 2: Enter: solve(x-5y=2 and 2x+y=4,{x,y})
Step 3: Write down what it tells you: x=2 and y=0

:)

I understand everything just fine, except for one part which is just something im doing wrong and I shouldt be.

In Xantars Explination, he gets 2-5y=2.

now its obvious y=0, but for some reason when I solve that the proper way, I dont come up with that. So sombody please explain how to get y=0 for that....

Because if y is equal to zero, then it'd be 2-(5 x 0)=2. 5 x 0= 0. So you check, and 2-0=2, so it's correct.

But you said it was obviously zero, so you probably already knew that. :D So I don't really know what you're asking now...

Jason1:

I can't help you unless you post the steps you took and the numbers you got. Otherwise, all I can say is "You did it wrong. Try it again."

I remember what I had a hard time with this.. it was only a month ago.. :D

eh, who cares, Ill just choose the other problem, and then everything is all okely dokely!

And Xantar, you asked why my parents cant help me, well thats because my mom was horrible at math as a Kid, and she still is today, she has trouble doing my brothers 5th grade math.

My dad was fairly smart, but hes forgotten everything, he cant help me either(except on some rare occasions)