Tiffany'sTerrificMath

Hello! My name is Tiffany S.  I am in Mrs. Felz's Algebra II Class. This project is designed to help you learn about word problems ,substitution, and the elimination method .
Elimination Method
To solve a problem by elimination you need make one of the variables able to cancel out.  To do this I multiplied the top row by 2. The reason why I did this is so that the fours will cancel each other outfor later on.  Now you have two new problems. The y's cancel each other out and you have 17 x equals 17.  Then you divide 17x by 17 to each side. 17 divided by 17 equal 1.  So x equals 1.  Next, you substitute 1 wherever x is in either one of the the original problems. When you do this you will be able to find the other variable. In this case it is y. 
7x+2y=-1
3x-4y=19

7x(2)+2y(2)=-1(2)

14x+4y=-2
3x-4y=19

17x=17
17x/17 17/17
x=1

7(1)+2y=-1
7+2y=-1
-7    -7
2y=-8
2y/2  -8/2
y=-4

 
        
Substition Method

To use the substitution method, you first need to put what x equals in place of the the x in the first equation.  So 3x(3y+10)+2y=8. Once you have this you will work the problem out as a normal equation. You will combine the "y's" and subtract 30 from eight.  Then you divide -22 by 11 to get -2. Y=-2.  Once you have the "y" you put it into the original equation and work it out as a normal algebra equation. This time you should get the "x".  To check this put the x and y in the equation to see if they equal the same thing. 
 

 3x+2y=8
x=3y+10

3(3y+10)+2y=8
9y+30+2y=8
11y+30=8
      -30  -30
11y=-22
11y/11=-22/11
y=-2

3x+2y=8
3x+2(-2)=8
3x+-4=8
     +4   +4
3x=12
3x/3=12/3
x=4
Linear Word Problem
The sum of a certain number and a second number is -42. The first number minus the second is 52. Find the two numbers.

First, I added "y" from the second equation to the side where the 52 is.  This is how I got what "x" equaled. Next, I put what I got for "x" into the first equation. After I did this I solved for the "y". After I got the "y" I substituted what "y" equaled in the "y" spot. This is how I got the "x". Then I put both of the numbers in to make sure they equaled -42. 

x+y=-42
x-y=52
  +y  +y
x=1y+52

1y+52+y=-42
2y+52=-42
     -52   -52
2y=10
2     2
y=5

x+5=-42
  -5    -5
x=-47

To Check:
-47+5=-42

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