Chapter 6

 Pg. 364 – 369  Obj: Learn how to solve systems of equations by graphing and analyze special systems.  Content Standard: A.REI.6

 System of Linear Equations – two or more linear equations  Solution of a System of Linear Equations – any ordered pair that makes all of the equations in a system true  Consistent – a system of equations that has at least one solution  Independent – a consistent system that has exactly one solution (intersecting lines)  Dependent – a consistent system that has infinitely many solutions (same line)

 Inconsistent – a system of equations that has no solution (parallel lines)

 Pg. 372 – 377  Obj: Learn how to solve systems of equations using substitution.  Content Standard: A.REI.6

 Substitution Method  Solve one of the equations for one of the variables  Substitute the expression for the variable  Solve for the variable  Use the solution to solve for the remaining variable  Check your solution

 Pg. 378 – 384  Obj: Learn how to solve systems by adding or subtracting to eliminate a variable.  Content Standards: A.REI.5 and A.REI.6

 Elimination Method  Add or subtract the equations to eliminate one of the variables  Solve for the remaining variable  Substitute the value into one of the original equations and solve

 Pg. 387 – 392  Obj: Learn how to choose the best method for solving systems of linear equations.  Content Standards: A.REI.6, N.Q.2, N.Q.3, and A.CED.3

 Choosing a Method for Solving Linear Systems  Graphing – When you want a display of the equations or when you want to estimate a solution.  Substitution – When one equation is already solve for one of the variables, or when it is easy to solve for one of the variables.  Elimination – When the coefficients of one variable are the same or opposites, or when it is not convenient to use graphing or substitution.

 Pg. 394 – 399  Obj: Learn how to graph linear inequalities in two variables and use linear inequalities when modeling real-world situations.  Content Standards: A.REI.12 and A.CED.3

 Linear inequality – can be formed by replacing the equal sign in a linear equation with an inequality symbol  Solution of an Inequality – an ordered pair that makes the inequality true

 Pg. 400 – 405  Obj: Learn how to solve systems of linear inequalities by graphing and to model real- world situations using systems of linear inequalities.  Content Standard: A.REI.12

 System of Linear Inequalities – made up of two or more linear inequalities  Solution of a system of linear inequalities – an order pair that makes all the inequalities in the system true  Method  Graph each line  Dashed - > or <  Solid - > or <  Choose a test point for each inequality and shade appropriately  Where the shading overlaps is the solution