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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


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)


Subtraction

10s + 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)