Notes – 2/13Addition Method ofsolving 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” variable3x = 9

Now solve for x. 3 3

x = 3Now solve for y using x = 3 Either equation can be used but the 2nd is simpler.

x – y = 1 3 – y = 1-3 -3 -y = -2 y = 2

Solution is (3, 2)

Example 2

3n – 2p = 63n – 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 5p = 2

Now solve for n with p = 2

3 n – 2p = 63n – 2(2) = 63n – 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 = 33 – y = 2-3 -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) = 02a + 6 = 0 -6 -62a = -6 a = -3 (-3,-2)