P.L.'s Math For Dummies
This web page is for the uneducated people like me in our society.

Solving Systems by Subsitution

Problem 1: 5x - 2y = 4
                  3x + y = 9		 Look at the two equations. Which one contains a single variable. Take that equation and put it in y = form.
Ex: y = -3x + 9

 
 

Plug in the equation with the other as y.
Ex: 5x - 2(-3x + 9)= 4
Complete the equation.
Ex:5x - 2(-3x + 9)= 4
5x + 6x - 18 = 4
11x = 22
x = 2

 
Plug in 2 as x in the equation.
y = -3x + 9
y = -3(2) + 9
y = -6 + 9
y = 3
Your final answer would be
(2,3).
 
Solving Systems by Linear Combination
 


Ex. 3x - 4y = -1
     -3x + 2y = 0
The first equation tells us that 3x - 4y = -1 are equivalent expressions.You can use the addition property to add the same quantity to both sides of the second equation. Then you can add 3x - 4y to the left side and -1 to the right side of the second equation.
-3x + 2y + (3x - 4y) = 0 + 1(-1)
You have actually added one multiple of the first equation to one multiple of the second equation. It is usually easier to add equations in this way.
3x - 4y = -1
-3x + 2y = 0
       -2y = -1
y = 1/2
Next, you subsitute 1/2 for y in either of the original equations.
-3x + 2y = 0 
-3x + 2(1/2) = 0
-3x + 1 = 0
Solving for x, you find x = 1/3
(1/3,1/2)
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 
5x + 9.75y = 398.75
5x + 9.75(-x + 45) = 398.75
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