07-3+Elimination+Using+Addition+and+Subtraction



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)]