Dustin's SpiffyMath
This web page is for my math class. My teacher is making me teach needy people who don't know easy algebra.
Substitution
Problem: y = 5 - 4x
              3x - 2y =12
2.   3x - 2(5 - 4x) = 12		 Look at the problem. Make one of the 
equations equal to one of the varables. Next take the problem following the 
varable that is alone and substitute it for the same varable in the other problem.

3. 3x - 10 + 8x = 12
4. 11x - 10 = 12
            +10  +10
5. 11x = 22
    11x/11 = 22/11
6. x = 2
7. y = 5 - 4(2)
  y = 5 - 8
  y = -3
8. (2,-3)
8
888
 

 

 Next work the problem out to fin x.
Next put answer to x in place of x in the problem that equals y.
 This will give you the answer to y.
Then put it in (x,y).
                                                       Linear Combination
 
1. x + y = 9 
  2x - y = -3
2. 3x = 6
3. 3x/3 = 6/3
4. x = 2
5. 2 + y = 9
6. 2 + y = 9
   -2          -2
y = 7
7. (2,7)		 1. You look at the problem and see if you are going to need multiply either of the problems to make one varable cancle.
2.Add the problems together.
3.This should give you a lone varable and a constant.
4.Find the answer to a varable's value.
5.Next substitute it in it's place in one of the problem's.
6.Find the other varable's value.
7.Put it in (x,y)
                                         Word problem
 
1.One day a store sold 45 pens, one kind at $8.50 and another kind at $9.75. In all $398.75 was taken in.How many of each kind were sold.

2.Find the first equations. X + Y = 45
3. Find the second equation.
4.Plug in the numbers found in the problem.
5.Substitute the problem that equals y in the problem.
6.Then multiply it out. 
7.This will give you the answer to the x.
8. Put this in place of the x in the other equation. 
9.This will give you the answer to the y.

 X + Y = 45
y = -x + 45 
8.5x + 9.75y = 398.75
8.5x + 9.75(-x + 45) = 398.75
8.5x - 9.75x + 438.75 = 398.75
-1.25x + 438.75 = 398.75
              -438.75   -438.75
     -1.25x = -40
x = 32
32 + y = 45
-32         -32
y = 13