Zach's Wonderful Equations

Welome to my website while your here why not learn something!

Hi have decided to save you a little touble with helping you with a few example of equations.  The first example I am going to show you is of a subsitution problem. By the way this is algebra two material.

All right let us go to the world of subsitution.
x = 3 - 3y
4y = x + 11
4y = (3 - 3y) - 11
7y = 14
y = 2
8 = x + 11
-3 = x
(-3,2)
All right lets tackle the equation!
  • Alright the first step is to isolate one of the variables.
  • This is easy because the top equation already has one isolated.
  • Alright the next step is to subsitute.
  • ok know let us isolate the y by combining like terms
  • The next step is to finish isolating the y by division.
  • Now we have the y lets get the x.
  • Subsitute the 2 for the y in the second equation.
  • solve for x.
   Alright  now let us go to the next equation.
 
 
Next we are going to do some linear equations. I personaly like these a little better and who knows maybe you will to. Linear Equations:
5x - 2y = 4
 3x   +  y = 9
These are the new formed equations.
5x - 2y = 4
6x + 2y = 18
11x = 22
x = 2
3(2)+ y  =9
y = 3
(2,3)
  1. Alright the first step is to cancel out one of the varibles.
  2. ok the y looks the easiest because there is already a + and  - y.
  3. In order to do this you need to to get the y equal.
  4. to get it equal you have to multiply the top by 1 and the bottom by 2.
  5. Alright know lets cancel the y, and create a new equation, and with this new equation solve for x.
  6. know with the x found subsitute it in one of the original equations. ( I am going to use the bottom one.) 
  7. good job!!!!!!!!!!!!!!
one more to go.
the last one is a word problem !!!!! This one will be easy.
The difference between two numbers is 16.  Three times the larger number is nine times the smaller. what are the numbers? Alright, on this you will first need to make two equations.

x-y = 16
3x = 9y  /    3x-9y = 0
Now you have your two equations and you can either use subsitution or linear.
I am going to show it to you in the linear form First.

x-y = 16        cancel the y's first
3x-9y = 0       multiply top by 9 and bottom by -1.

9x - 9y = 144            6x = 144
-3x + 9y = 0               x =   24

put back in the 24 in either of the original equations.

24 - y = 16       16-24
-y = -8 
y = 8                          ( 24,8)

i'll let you try subsitution.
 

NOW YOU HAVE ACCOMPLISHED THREE WAYS OF SOLVING EQUATIONS.

CHECK OUT THE LINK TO GET MORE HELP.

 PURPLEMATH.COM

For info on my school go to

 www.henry.k12.ga.us/ugh/