7.5 Solve Special Types of

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1 75 Solve Special Tpes of Linear Sstems Goal p Identif the number of of a linear sstem Your Notes VOCABULARY Inconsistent sstem Consistent dependent sstem Eample A linear sstem with no Show that the linear sstem has no solution 22 5 Equation 22 5 Equation 2 To ease graphing, write each equation in slope intercept form Method Graphing Graph the linear sstem are because the have the same slope but different -intercepts Parallel lines do, so the sstem has Method 2 Elimination Subtract the equations The variables are and ou are left with a regardless of the values of and This tells ou that the sstem has 86 Lesson 75 Algebra Notetaking Guide Copright Holt McDougal All rights reserved

2 75 Solve Special Tpes of Linear Sstems Goal p Identif the number of of a linear sstem Your Notes VOCABULARY Inconsistent sstem A linear sstem with no Consistent dependent sstem A linear sstem with infinitel man Eample A linear sstem with no Show that the linear sstem has no solution 22 5 Equation 22 5 Equation 2 To ease graphing, write each equation in slope intercept form Method Graphing Graph the linear sstem are parallel because the have the same slope but different -intercepts Parallel lines do not intersect, so the sstem has no solution Method 2 Elimination Subtract the equations The variables are eliminated and ou are left with a false statement regardless of the values of and This tells ou that the sstem has no solution 86 Lesson 75 Algebra Notetaking Guide Copright Holt McDougal All rights reserved

3 Eample 2 A linear sstem with infinitel man Show that the linear sstem has infinitel man 5 Equation Equation 2 Method Graphing Graph the linear sstem The equations represent the, so an point on the line is a solution So, the linear sstem has Method 2 Substitution 5 Solve Equation for Write Equation 2 ( ) Substitute for Distributive propert 5 29 Simplif The variables are and ou are left with a statement that is regardless of the values of and This tells ou that the sstem has Copright Holt McDougal All rights reserved Lesson 75 Algebra Notetaking Guide 87

4 Eample 2 A linear sstem with infinitel man Show that the linear sstem has infinitel man 5 Equation Equation 2 Method Graphing Graph the linear sstem The equations represent the same line, so an point on the line is a solution So, the linear sstem has infinitel man Method 2 Substitution 5 2 Solve Equation for Write Equation 2 ( 2 ) Substitute 2 for Simplif Distributive propert The variables are eliminated and ou are left with a statement that is true regardless of the values of and This tells ou that the sstem has infinitel man Copright Holt McDougal All rights reserved Lesson 75 Algebra Notetaking Guide 87

5 Checkpoint Tell whether the linear sstem has no solution or infinitel man NUMBER OF SOLUTIONS OF A LINEAR SYSTEM One solution No solution Infinitel man Homework have slopes are have the same slope and -intercepts have the same slope and the 88 Lesson 75 Algebra Notetaking Guide Copright Holt McDougal All rights reserved

6 Checkpoint Tell whether the linear sstem has no solution or infinitel man infinitel man no solution NUMBER OF SOLUTIONS OF A LINEAR SYSTEM One solution No solution Infinitel man Homework intersect have different slopes are parallel have the same slope and different -intercepts coincide have the same slope and the same -intercept 88 Lesson 75 Algebra Notetaking Guide Copright Holt McDougal All rights reserved

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