Algebra ( Period 5)

Using Addition to Solve a System 6-3

The second Algebraic method to solve a system is known as ELIMINATION
You will be eliminating one variable by using the ADDITIVE INVERSE of it in the other equation

4x + 6y = 32
3x -6y = 3

7x + 0 = 35
7x = 35
x = 5

Plug into EITHER equation to find y
4(5) + 6y = 32                   20 +   6y = 32               
6y = 12                      y = 2
So the solution is ( 5, 2)

Sometimes you almost have additive inverses, but you need to multiply ONE EQUATION by -1 ...FIRST

5x + 2y = 6
9x + 2y = 22

Multiply EITHER the Top or the Bottom by -1 (Your choice)

5x + 2y = 6
-9x -2y = -22

-4x + 0 = -16                  

-4x = -16
x = 4

Plug into either ORIGINAL equation

5(4) + 2y = 6   so 20 + 2y = 6
2y = -14 

y = -7
The solution is ( 4, -7)

Now you can plug this point into the other equation to check that you haven’t made a mistake:  9x + 2y = 22  

9(4) +2(-7) = 2   

36 – 14 = 22  YES!!!