System of Linear Equtions

Solving systems with two variables

1. Graph
- find intersection which is the place both equations share the same x, and y.
x-y-1=0 2x+y=-4
x-1=y -2x-4=y
Graph the above equations, 2nd trace, 5:intersect, enter, enter, enter, then you can get the intersection there.
intersection ( -2, -1 )

2. Elimination
5x+4y=6
-3y-2x=1
step 1 : Rearrange each equation, so variables are in same column.
5x+4y=6
-2x-3y=-1
step 2 : Multiply equations by appropriate value to eliminate one variable.
15x+12y=18
+ -8x-12y=-4
___________
7x+ 0y=14
7x =14
x=2

step 3 : Substitute variable into either of the original equations to solve for second variable.
5(2)+4y=6
4y=6-10
4y=-4
y=-1
solution : ( -1, 2 )

step 4 : Check - use calculator to check the answers.

3. Substitution
4x+y=1
2x-3y=4
step 1 : Solve one of the equations for one variable.
4x+y=1
-4x+1=y
step 2: Substitute this expression into other equation.
2x-3y=4
2x-3y(-4x+1)=4
2x+12-3=4
14x=7
x=1/2
y=-4(1/2)+1
y=-2+1
y=-1
solution (-1, 1/2 )

algebra

I guess this unit was okay. Solving x. I found the hardest thing is to remember some equations. Sometimes I was confused which equation is which topic's. By looking at the math dictionary, understood. ^.^

algebra

hey guys.. well i guess this unit was overall okay. Although spring break kind of ruined it for me, due to the fact that it made me forget everything. Anyways, I think the most difficult part of this unit, is having to remember everything and being able to differentiate between each topic because there were so many concepts to comprehend. Other than that, that;'s pretty much it.

Algebra was okay, it was pretty long though. A lot of things needed to be remembered but overall it was straight forward and easy.. or so I say.. hopefully I'll pass the test =) Doing the dictionary was helpful because it allowed me to review all the things we learned.

algebra..

hi there..algebra is a part of the unit that i've already took. Although our teacher discussed this clearly i still have a hard time in solving some equations..Hopefully, i will pass our test today..wish me luck! hehe

algebra

hi classmates..I thought algebra is one of the easiest part of the unit because you just have to find the value of x. But i have noticed that i have had a hard time to solved some of the equations. It's quite easy but pretty challenging though. anyways, goodluck!!

blogging on blogging #3

Algebra is my favorite part of the unit because we just simply solving for x. Although I'm having hard time to solve it. I'm still trying my best to do it.. Im doing good in this unit, so i think I'll be fine in the test. Good luck everybody.

So overall, I thought this concept was overall quite easy. Although there were some parts where I didn't quite understand thoroughly, I just re-read over my notes and follow the directions to solving the equations, and understood it.

Algebra Unit Reflection

At the beginning of this unit I thought it was easy, well until the numbers got a little too big... I mostly make minor mistakes, but I'll live. I just need to find out why I keep on making these mistakes. Thats the end of this, good luck everybody!

ALGEBRA UNIT REFLECTION

Hi boys and girls. I thought this "algebra unit" was easy at first, until spring break came along and ruined everything. I found that it was easy to comprehend, however, the concepts were difficult to initiate (unless you could remember the proper steps). Imaginary numbers and radical equations were the hardest topics in this unit for me. The easiest topic was the x2+b/a+c/a=0 stuff. Yeah whatever. Anyways, good luck on the test everybody.

Algebra Unit Reflection

Hm, the algebra unit. To be honest, I completely forgot that this unit was called algebra - that is probably partially due, or completely due, to the fact that spring break cut this unit into two nifty pieces. Anyways, I found that a lot of aspects in regards to the algebra unit were fairly easy to understand, they're just concepts which are much harder to initiate unless you can remember the exact steps in rearranging or breaking down the equation. I wasn't too big on imaginary numbers or complex numbers either, roots don't really tickle my fancy. I still don't even understand this discriminant thing either, well, maybe if I review my notes .. Anyways, algebra as a while wasn't too bad, it definitely wasn't as complicated to me as the first unit that we had. Everyone, good luck on your test tomorrow - I'll need it. Haha, and have a good spirit week you guys. Good night. :)

Algebra Reflection

Overall, this unit wasn't too difficult, with maybe some minor difficulty here and there...cough long equations...but after today's pretest, I realized the only difficulty I actually had was remembering certain parts to the problem. Namely all the steps to solve the problem or the minor things you can easily forget (like -b/a). So good luck tomorrow on the test everyone, even though it shouldn't be luck that gets us through it anymore. ;D

Algebra Unit Reflection

LONG .. that's the word to describe it. I don't know if it's because of Spring Break but it seems like such a long unit. There were a lot of things that had to be learned. The hardest part for me was hmm, determining which one's which, and what is the right simplification that will give me the correct answer. Good luck to me and to all of you tomorrow! (: *cough*

algebra

Hi guys! I'm blogging for our test tomorrow. Well anyways this unit was pretty easy. After I looked over my notes I got pretty much everything. I just hope I do good on the test tomorrow! The most difficult part for me was probablyrational equations and determining the restrictions. Well that's it, good luck to everyone tomorrow!

Algebra Reflection

Algebra is difficult in some points because of things like today's pretest that shows I need to study more. Algebra isn't too hard but you have to get the hang of the different formulas and such. After knowing those, you just have to work at it or so I tell myself. The hardest parts were when the questions got pretty long especially with rational equations and you had to square the fractions constantly until something actually made sense. That was the most annoying thing that I couldn't solve. Oh well. Keep studying and good luck on tomorrow's test, everyone!

ALGEBRA

So overall, I thought that this concept was okay. After reading over my notes and a few examples I think I'm starting to get the hang of it. It was a little difficult, especially the radical equations for myself. But other than that I thought this unit was okay.

-Sheena

** ALgebra is hard.. well I understand some part of it... The rational equation is pretty confusing especially the fractions. Well I hope that all of us will pass the test.. goodluck! **

Radical Equation

Hi classmates! This is Djanine and I'm the scribe for today. Well Ms. Ingram talked about radical equation. What is a Radical Equation???

A "radical" equation is an equation in which the variable is stuck inside a radical.

When you have a variable inside a square root, you undo the root by doing the opposite: squaring. For instance, given , you would square both sides:

Examples:

a. 3 + 4 = 7

(3 + 4)2 = 72

49 = 49

Square both sides.

You should always remember to: SQUARE SIDES, NOT TERMS.

b. √4=2
Square both sides.
(√4)2 =(2)2
4=4

Always remember to get rid the radicals.

c. (√18-3x)2=(6)2

Use the Foil method=square 6

18-3x=36
-3x=36-18

Divide them by -3.

X=-6

d. (4√x+2)2=(32)2
16x+32=1024
16x=992

Divide them by 16.

So x will be 62.

The next scribe is Brian L.

By the way, we have a test on Wednesday (April 11).