Systems of Linear Equations in Two Variables

Ok, today in class we did something like the Friday's class. We practiced doing the different techniques on how to solve systems of linear equations in two variables.

We were given three systems to solve:

x=y+6
3x-5y=7

3x+2y=16
y+7x=19

2x+3y=4
5x+2y=3

Ok, lets do the first one. This first question is best suited to be answered using the substitution technique, because as you can see there is a equivalent for the x value.

x=y+6
3x-5y=7
3(y+6)-5y=7
3y+18y-5y=7
-2y=-11
y=11/2
x=11/2+6
x=11/2+12/2
x=23/2

Therefore, these lines intersect at (23/2,11/2).

Now, lets do the second one.This certain question is best suited to be answered using the elimination technique , because there is no equivalent on any of the variables unlike the first one.

3x+2y=16
y+7x=19

3x+2y=16
7x+y=19
-11x=-22
x=2
7(2)+y=19
y=5

Therefore,these lines intersect at (2,5).

Lastly, before we do some word questions. This question is suited to be answered using the elimination technique just like the second one.

2x+3y=4
5x+2y=3
-11x=-1
x=1/11
3y=4-2x
3y=44/11-2/11
3y=42/11
y=14/11

Here we go again with this word questions....

125 tickets were sold at a basketball game. A total of $337.50 was collected. Students paid $2.50/ticket and other people paid $3.50. How many students attended the game?

Let s=# of student's tickets
p=#of other people's tickets

2.50s+3.50p=337.50
s + p =125
-s =-100
s=100

Therefore , there are 100 student tickets and 25 other people's tickets.

After doing all the warm up things Mr. K started talking about consistent and inconsistent lines.
A consistent line means that there is an answer.It can be break up into a dependant and an independant line. Independant means that there is only one solution. Dependant means that there is an infinite amount of solutions. An inconsistent line means that there is no solution.

I'll be editing this tomorrow because the html codes for line 1 and line 2 doesn't seem to work.

The scribe for tomorrow is ............... "SAMUS" .

Sorry SAMUS ,but you're the one that pop into my hEAD first. I was gonna pick Lauressa but she said her computer wasn't working...

Homework for tonight is Exercise 25 excluding questions number 1 and 2.