1. 7.3 Elimination Using Addition and Subtraction What you’ll learn: 1.To solve systems of equations with addition 2.To solve systems of equations with subtraction

2. Elimination The goal of solving a system through elimination is to eliminate one of the variables. To eliminate a variable, add the equations together if one set of variables is opposites such as 4x and -4x.

3. Elimination using addition 1.Find a pair of like-variables that are opposites. 2.Add the equations together which eliminates that variable. 3.Solve the equation. 4.Plug in to find other variable. Example:3x+2y=4 2x-2y=6 5x=10 x=2 3(2)+2y=46+2y=42y=-2 y=-1 solution: (2,-1)

4. examples 1.-x+y=2 x+2y=-8 3y=-6 y=-2 -x+(-2)=2 -x-2=2 -x=4 x=-4 Solution: (-4, -2) 2.5x-2y=11 5x+2y=-21 10x=-10 x=-1 5(-1)-2y=11 -5-2y=11 -2y=16 y=-8 Solution: (-1,-8) + +

5. Elimination using subtraction When opposites are not given, but the coefficients of like-variables are the exact same, use subtraction. 1.Locate same coefficients on like-variables. 2.Change the signs of all the terms in one of the equations. (not both!) 3.Continue as elimination using addition.

6. Examples 1.4x+2y=1 5x+2y=3 Change one equation to opposites: 4x+2y=1 -5x-2y=-3 -x=-2 x=2 4(2)+2y=1 8+2y=1 2y=-7 y=-3.5 Solution: (2,-3.5) 2.x+y=3 x+2y=5 change to: x+y=3 -x-2y=-5 -y=-2 y=2 Substitute in to find x: x+2=3 x=1 Solution: (1,2)

7. Mixed problems 1.-3x+4y=12 3x-6y=18 3.3x-9y=-12 3x-15y=-6 2.4x+2y=28 4x-3y=18

8. Classwork p. 385 4-8 even, 12-32 even