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8-3 Addition method AKA Combination or Elimination 9P9: Solve 2X2 systems by elimination Steps 1) 2) 3) 4) 5) 6) 7) Put both into standard form (Ax+By =C) and stack Multiply 1 (or both) equation(s) to make opposites Add (combine) the equations (one var is eliminated) Solve for the remaining variable Put that value in (either equation) solve for other variable Write solution as ordered pair Check Example 1 Remember to solve for second variable You can use either equation! x+y=5 + 2x - y = 4 3x 3 =9 3 x =3 3+y=5 -3 -3 y=2 The solution is (3,2) Example 2 7x – 5y = 76 ( 4x + y = 55 )5 We need opposites here. 7x – 5y = 76 + 20x + 5y = 275 4(13) + y = 55 27x 52 + y = 55 27 y=3 The solution is (13,3) = 351 x = 13 27 Example 3 ( 2x + 3y = 20 )3 ( 3x + 5y = 37 )-2 Here we need to change both equations By making x’s 6 or y’s 15 6x + 9y = 60 + -6x -10y = -74 2x + 3(14) = 20 2x + 42 = 20 2x = -22 x = -11 The solutions is (-11,14) -1y = -14 y = 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. To get rid of fractions use the LCD N1: x N2: y ( x - y = 36 )-3 -3x + 3y = -108 ( 1 x 1 y 11)18 6 9 + 3x - 2y = 198 x – 90 =36 x = 126 The numbers are 126 and 90 y = 90 assignment 8-3/ 371/ 1-12 Assignment 8-3/371/15-39 odd, 50-58 even Quiz tomorrow 8-1 to 8-3