You use elimination to solve systems of equations. Sometimes when adding two equations together, a variable is eliminated. When you use this step to solve an equation, it is called elimination. You can either eliminate a variable while using subtraction or addition.

Addition

2x - 12y = 36 <-- Since these coefficients are additive inverses
4x + 12y = -24 you eliminate the terms by adding both equations together

You use elimination to solve systems of equations. Sometimes when adding two equations together, a variable is eliminated. When you use this step to solve an equation, it is called

elimination.You can either eliminate a variable while using subtraction or addition.Addition2x - 12y = 36 <-- Since these coefficients are additive inverses

4x + 12y = -24 you eliminate the terms by adding both equations together

2x - 12y = 36

4x + 12y = -24

(+)6x = 12

--> variable is eliminated--- ---

6 6

x = 2

Now you can substitute 2 for x in either of the above equation solve the equation to find the value of "y"

4x + 12y = -24

4(2) + 12y = -24

8 + 12y = -24

-8 -8

12y = -32

--- ----

12 12

y = -2 2/3

Your final solution is (-2,2/3)

Subtraction10s + 5t = 25 <-- Since the coefficients are the same you eliminate them by subtraction

25s + 5t = 45

10s + 5t = 25

25s + 5t = 45

_(-)_35s = 70

--> variable is eliminated--- ---

35 = 35

s = 2

Now you can substitute 2 for s in either of the above equations

10s + 15t = 25

10(2) + 15t = 25

20 + 15t = 25

-20 -20

15t = 5

--- ---

15 5

t = 1/3

Your final solution is (2, 1/3)

07-3 Elimination Using Addition and Subtraction

07-3 Elimination Using Addition and Subtraction(2)