7 3 Elimination Using Addition and Subtraction What

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

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 4 x and -4 x.

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: 3 x+2 y=4 2 x-2 y=6 5 x=10 x=2 3(2)+2 y=4 6+2 y=4 2 y=-2 y=-1 solution: (2, -1)

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

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.

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

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

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