Examples 
 
This Example can help you in your day to day work!
Linear Combination: 
Explanation in words 
You take two equations and make it where you can take away one of the variables.  Then you find X.  You now take X and plug it in to one the original equations.  Now you must find Y. Once you find X and Y this will be your answer. 
Example 
5x-2y=4 
3x+y=9 
You must get rid of a variable: 
5x-2y=4 
2(3x+y=9) 
equals
5x-2y=4                        or                   5x=4 
6x+2y=18                                            6x=18 
The -2y and the 2y cancel out  
11x=22 
You add like kinds 
11x/11=22/11 
x=2 
Now "plug it in" 
5(2)-2y=4 or  10-2y=4 
Take away 10 from both sides 
-2y=-6 
divide -2 from both sides 
y=3 
Your answer is (2,3)

 
Substitution Method: 
Explanation in words 
The first thing you need to do is take the problem that has an X or a Y already found.  Then take that problem and plug it in to the other problem. Once you find what a variable is plug the answer into the other problem.

 
 
Example: 
x-5y=10 
-2x+y=7......y=2x+7 
x-5(2x+7)=10 
x-10x-35=10 
-9x-35=10 
-9x=45 
x=-5 
Now plug -5 in to get Y!!! 
-5-5y=10
add 5 to both sides
-5y=15
y=-3

 
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