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Table of Contents Topic ... Page # 6.6A Absolute Value Less ThAND 6.6B Absolute Value GreatOR Than 6.7 Two Variable Inequalities 7.1 Solve Systems By Graphing 7.2 Solve Systems By Substitution 7.3 Solve Systems By Combination 73 74 75 76 77 78 Solve Systems by Substitution: 1) Line up the x and y values in standard form 2) Make one variable opposite each other if needed 3) Add the equations 4) Solve for the variable 5) Plug answer into any equation to find the other variable 6) Write answer as ordered pair (x,y) Example 1: Rewrite the linear system so that the like terms are arranged in columns a. 3x – y = 23 y + 8x = 11 3x – y = 23 8x + y = 11 Example 1: Rewrite the linear system so that the like terms are arranged in columns b. 4x = y + 1 3y + 4x = 7 4x – y = 1 4x + 3y = 7 Example 1: Rewrite the linear system so that the like terms are arranged in columns c. 7x – y = 13 y = 14x - 3 7x – y = 13 -14x + y = -3 Example 2: Use the linear combination method to solve the system. + 2x + 3y = 11 -2x + 5y = 13 8y = 24 y=3 2x + 3(3) = 11 2x + 9 = 11 2x = 2 x=1 (1, 3) ans:_______________ + 6x – 4y = 14 -3x + 4y = 1 3x = 15 x=5 -3(5) + 4y = 1 -15 + 4y = 1 4y = 16 y=4 (5, 4) ans:_______________ + 4x – 3y = 5 –2x + 3y = -7 2x = -2 x = -1 -2(-1) + 3y = -7 2 + 3y = -7 3y = -9 y = -3 (-1, -3) ans:_______________ Example 3: Use the linear combination method to solve the system. 3x + 4y = -6 2y = 3x +6 3x + 4y = -6 + -3x + 2y = 6 6y = 0 y=0 3x + 4(0) = -6 3x = -6 x = -2 (-2, 0) ans:_______________ 8x – 4y = -4 4y = 3x + 14 8x – 4y = -4 + -3x + 4y = 14 5x = 10 x=2 -3(2) + 4y = 14 -6 + 4y = 14 4y = 20 y=5 (2, 5) ans:_______________ -5y = -4x – 6 2x + 5y = 12 + 4x – 5y = –6 2x + 5y = 12 6x =6 x=1 2(1) + 5y = 12 2 + 5y = 12 5y = 10 y=2 (1, 2) ans:_______________