Systems of Equations: By Trevor
 
 
 

This site is for a grade.  Mrs. Felz is making me create it.
Linear Combination:
                                                                                         
Find the value of x & y.                                                      
How to get y.

-3x+7y = -1                  -2(-3x+7y = -1) 6x+-14y = 2 2
-2x+5y = 0                      3(-2x+5y = 0) -6x+15y = 0+0  2
                                                                        1y        2   1
                                       y = 2 
                                       next 

      To get y, you multiply -2(-3x+7y = -1).  Then you multiply
3(-2x+5y = 0).  Your new equations should be 6x+-14y = 2 and -6x+15y = 0.  You add the y numbers together and you should get 1y.  Next you add the answers together and you should get 2.  
How to get x.

-3x+7y = -1                   -5(-3x+7y = -1) 15x+-42y = 5  5&nbbsp;
-2x+5y = 0                       7(-2x+5y = 0) -14x+42y = 0 +0
                                                                   1x                 5
                                                                               5 = 5
                                                                               1
                                         x = 5
The solution is  (5,2). 
Substitution:

Find the value of x & y.
How to get x.

x-5y = 10                         x-5(2x+7) = 10
y = 2x+7                           x-10x-35 = 10
                                            -9x-35 = 10    &nbssp; 
                                                -9x = 45
                                                   x = -5  
                                                    next
How to get y.

                                               y = 2x + 7
                                              -10+7 = -3
                                                   y = -3
 x-5y = 10
1(-5)-5(-3) = 10
-5+15 = 10

The solution is   (-5,-3).