8.3 The Addition Method Also referred to as Elimination Method.

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Presentation transcript:

8.3 The Addition Method Also referred to as Elimination Method

The Addition Method Write the second equation below the first. Add the equations together and solve for the remaining variable.

Solve: + x + y = 5 x - y = 1 x - y = 1 x - y = 1 x - y = 1 x - y = 1 = 6 x = 3 3 + y = 5 y = 2 (3,2)

x + y = 5 x + y = 5 2x - y = 4 3x = 9 x = 3 3 + y = 5 y = 2 (3,2)

2 Special Cases No solution Case 1: NO SOLUTION Both variables cancel out but the constant does not Leaving a false equation. 4x - 2y = 2 -4x + 2y = -16 0 + 0 = -14 No solution

Case 2: INFINITELY MANY SOLUTIONS Both variables and the constant cancel out Leaving a true equation 5x - 7y = 6 -5x + 7y = -6 0 + 0 = 0 Infinitely many solutions

They all do not cancel out so easily If the equations do not eliminate a variable when you add them together: Multiply the whole equation by a number that will help you cancel it out.

2 4x - 2y = 7 4x - 2y = 7 3x + y = 4 6x + 2y = 8 10x = 15 x = 1.5 (1.5,-0.5)

-1 2x + 3y = 8 2x + 3y = 8 x + 3y = 7 -x - 3y = -7 x = 1 2(1) + 3y = 8 (1,2)

3 4 4x + 2y = 18 12x + 6y = 54 -3x + 5y = 6 -12x + 20y = 24 26y = 78 (3,3) y = 3

3 -5 5x + 3y = 2 15x + 9y = 6 -15x - 35y = 20 3x + 7y = -4 -26y = 26 (1,-1) x = 1

5(a-b)=10 and a+b=2

The sum of two numbers is 72. The difference is 58. Find the numbers. x + y = 72 x - y = 58 7 and 65

The sum of the length and width of a rectangle is 25 cm The sum of the length and width of a rectangle is 25 cm. The length is 2 less than twice the width. Find the length and width.

Assignment: Page 371 (2-40) even