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Table of Contents Topic Page #... 6.6A Absolute Value Less ThAND 73 6.6B Absolute Value GreatOR Than 74 6.7 Two Variable Inequalities 75 7.1 Solve Systems By Graphing 76 7.2 Solve Systems By Substitution 77 7.3 Solve Systems By Combination 78

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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)

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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

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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

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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

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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 ans:_______________ (1, 3)

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6x – 4y = 14 -3x + 4y = 1 + 3x = 15 x = 5 -3(5) + 4y = 1 -15 + 4y = 1 4y = 16 y = 4 ans:_______________ (5, 4)

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4x – 3y = 5 –2x + 3y = -7 + 2x = -2 x = -1 -2(-1) + 3y = -7 2 + 3y = -7 3y = -9 y = -3 ans:_______________ (-1, -3)

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3x + 4y = -6 2y = 3x +6 3x + 4y = -6 -3x + 2y = 6 + 6y = 0 y = 0 3x + 4(0) = -6 3x = -6 x = -2 ans:_______________ (-2, 0) Example 3: Use the linear combination method to solve the system.

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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 ans:_______________ (2, 5)

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-5y = -4x – 6 2x + 5y = 12 4x – 5y = –6 2x + 5y = 12 + 6x = 6 x = 1 2(1) + 5y = 12 5y = 10 y = 2 ans:_______________ (1, 2) 2 + 5y = 12

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