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7.3 Elimination Using Addition and Subtraction. What you’ll learn: To solve systems of equations with addition To solve systems of equations with subtraction. Elimination.
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7.3 Elimination Using Addition and Subtraction What you’ll learn: To solve systems of equations with addition 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 4x and -4x.
Elimination using addition • Find a pair of like-variables that are opposites. • Add the equations together which eliminates that variable. • Solve the equation. • Plug in to find other variable. Example: 3x+2y=4 2x-2y=6 5x=10 x=2 3(2)+2y=4 6+2y=4 2y=-2 y=-1 solution: (2,-1)
examples + + • -x+y=2 x+2y=-8 3y=-6 y=-2 -x+(-2)=2 -x-2=2 -x=4 x=-4 Solution: (-4, -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)
Elimination using subtraction When opposites are not given, but the coefficients of like-variables are the exact same, use subtraction. • Locate same coefficients on like-variables. • Change the signs of all the terms in one of the equations. (not both!) • Continue as elimination using addition.
Examples • 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) • 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)
Mixed problems • 4x+2y=28 • 4x-3y=18 • -3x+4y=12 3x-6y=18 • 3x-9y=-12 3x-15y=-6
