8-3 Addition method AKA Combination or Elimination 9P9: Solve 2X2 systems by elimination.

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Solve Systems of Equations by Elimination

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Presentation transcript:

8-3 Addition method AKA Combination or Elimination 9P9: Solve 2X2 systems by elimination

Steps 1) Put both into standard form (Ax+By =C) and stack 2) Multiply 1 (or both) equation(s) to make opposites 3) Add (combine) the equations (one var is eliminated) 4) Solve for the remaining variable 5) Put that value in (either equation) solve for other variable 6) Write solution as ordered pair 7) Check

Example 1 x + y = 5 2x - y = 4 + 3x = 9 3 x =3 Remember to solve for second variable You can use either equation! 3 + y = 5 -3 y = 2 The solution is (3,2)

Example 2 7x – 5y = 76 ( )5 We need opposites here. 4x + y = 55 7x – 5y = 76 20x + 5y = x = x = 13 4(13) + y = y = 55 y = 3 The solution is (13,3)

Example 3 2x + 3y = 20 3x + 5y = 37 Here we need to change both equations By making x’s 6 or y’s 15 ( )3 ( )-2 6x + 9y = 60 -6x -10y = y = -14 y = 14 2x + 3(14) = 20 2x + 42 = 20 2x = -22 x = -11 The solutions is (-11,14)

Which method would you use? Why? y = 2x – 6 3x = 3y -6

Write a system to solve The difference between two numbers is 36. One sixth of the larger number minus one ninth of the smaller number is 11. Find the numbers. N1: x N2: y x - y = 36 ( )18 3x - 2y = 198 ( )-3-3x + 3y = y = 90 x – 90 =36 x = 126 The numbers are 126 and 90 To get rid of fractions use the LCD

assignment 8-3/ 371/ 1-12

Assignment 8-3/371/15-39 odd, even Quiz tomorrow 8-1 to 8-3