Types of Linear Systems

~ Consistent System ~ ordered pair solution
lines intersect; meet at one point
slope of lines are different
intercepts are different unless intersection is on the
intercept



~ Inconsistent System ~ no solution
lines are parallel
slopes are the same
intercepts are all different



~ Dependent System ~ many solutions (infinitely)
lines are super imposed
slopes are the same
intercepts are the same




~ Slope Form ~
y = m(x) + b

~ Standard Form ~
A(x) + B(y) + C = 0

~ Point-Slope Form ~
y - y1 = m(x - x1)

Summary Of First Unit

The things i learned in this unit was:
The Algebracically way to solve things.
ex.
L1: y = 1/2x + 1
L2: y = -2x - 4

(1/2x = -2x - 5) 2
x = -4x - 10
(10)/-5 = (-5x)/-5
-2 = x

and since:
y = -2x - 4

we get:
y = -2 (-2) - 4
y = 4 - 4
y = 0
( -2 , 0 )

The Substitution Method:
L1: x - y = -1
L2: x + 2y = 8

L1: " "----------> x = (-1 + y)
L2: " "---------> ( -1 + y ) + 2y = 8
-1 + y + 2y = 8
-1 + 3y = 8
3y = 9
y = 3

Since y = 3 and since
x + 2y = 8

then x + 2 ( 3 ) = 8
x + 6 = 8
x = 2
the solution is ( 2 , 3 )

The elimination method is basically the same way excpt that you use addition or subtraction in the problem:
L1: 5x + y = 16
L2: 2x + 3y = 3

L1: " " ------>( 5x + y = 16 ) 3
L1: 15x + 3y = 48
ADD L2: 2x - 3y = 3

You get: 17x =51
x = 3

And since 5x + y = 16
5 ( 3 ) + y = 16
15 + y = 16
There fore: y = 1

The solution is ( 3 , 1 )

First Post Instructions

So the whole idea of having a classroom blog is to communicate meaningfully in a not-real-time way with your classmates and your instructor (me!). To that end, free marks on tests will be available when you create a post prior to a test that hopefully helps you to prepare for that test....I'm going to call these things unit summaries, and we'll have a few of these 'Unit Summary' posts due over the semester. The instructions for the first one follow:

Specifically, here's what I'm thinking you should include:

1. Format is negotiable, but sentence / paragraph makes sense to me...

2. I want to know, in a summarized, paraphrased, format, what you think (by skill list), what you think you were supposed to learn this unit.

3. I want to know specifically, what you are confident-with, skill-wise (so you don't study that), and what you are currently lacking skills with. This identification of needs may allow me (or classmates) to post things that may help.

4. Your impressions of the unit/section regarding presentation of material or general thoughts about ease or difficulty. Sharing with classmates creates community.

I would encourage thoughtful, sensitive, and intelligent commenting on each other's posts. Remember what my mother told me..."If you can't say anything nice..."

RM

***If your written submission exceeds 250 words, you're probably not summarizing well enough...

#3

The number of girls at Sky High School is 60 greater than the number of boys. If there are 1250 students all together, how many girls are there?

Let x = the # of girls
Let y = the # of boys

x + y = 1250 (y = 1250 - x)
y + 60 = x (y= x - 60)

Input it into your graphing calculator and you have your solution (almost). Good window settings are:
xmin = -10
xmax = -1500
ymin = -10
ymax = 1000

The solution is (655, 595), so there are 655 girls in Sky High School.

#5
first step:
let a=first number
let b=second number

Second step :
l1: a+(2a-3)=75

third step:
a+2a-3=75
3a/3=78/3
a=26
b=2a-3

b=2*26-3
b=49

Why Are There Rules in Croquet?

Please post solutions below as comments, or feel free to create a post indicating your number for your team...

RM

Welcome!!!

Hey everyone! Welcome to this semester's version of Grade 11 Applied Math on the web, blogger-style. The intention of this blog is to provide students (tutors, maybe parents, and anyone else interested) with the ability to interact and learn together.

"The whole is greater than the sum of the parts" (I'm not sure exactly whom to attribute that quote to.....Check out the video below if you missed class on Friday. I always think that it's a nice way to begin the semester.





RM