# Notes – 2/13 Addition Method of solving a System of Equations Also called the Elimination Method.

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Notes – 2/13 Addition Method of solving a System of Equations Also called the Elimination Method

Example 1 2x + y = 8 x – y = 1 Add the equations together to eliminate the “y” variable 3x = 9 Now solve for x. 3 3 x = 3 Now solve for y using x = 3 Either equation can be used but the 2 nd is simpler. x – y = 1 3 – y = 1 -3 -y = -2 y = 2 Solution is (3, 2)

Example 2 3n – 2p = 6 3n – 7p = -4 Addition doesn’t eliminate any variable but subtraction will eliminated the “n”. - ( ) 3n – 2p = 6 -3n + 7p = 4 Now you can add them and eliminate the “n”. 5p = 10 5 5 p = 2 Now solve for n with p = 2 3 n – 2p = 6 3n – 2(2) = 6 3n – 4 = 6 +4 +4 3n = 10 n = 3 1/3 Solution is (3 1/3, 2) Note same coefficient of 3

Try these: 1. 3x + y = 10 x - y = 2 2. 2a + 3b = -12 2a – 3b = 0 Solution: 3x + y = 10 x – y = 2 4x = 12 x = 3 3 – y = 2 -3 - y = -1 y = 1 Solution (3,1) 2a + 3b = -12 -(2a – 3b = 0) 2a + 3b = -12 -2a + 3b = 0 6b = -12 b = -2 2a – 3(-2) = 0 2a + 6 = 0 -6 -6 2a = -6 a = -3 (-3,-2)

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