SYSTEMS OF EQUATIONS AND INEQUALITIES Chapter 6 6

SYSTEMS OF EQUATIONS AND INEQUALITIES Chapter 6

6. 1 Solving Systems by Graphing � � � Pg. 364 – 369 Obj: Learn how to solve systems of equations by graphing and analyze special systems. Content Standard: A. REI. 6

6. 1 Solving Systems by Graphing � � � 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)

6. 1 Solving Systems by Graphing � Inconsistent – a system of equations that has no solution (parallel lines)

6. 2 Solving Systems Using Substitution � � � Pg. 372 – 377 Obj: Learn how to solve systems of equations using substitution. Content Standard: A. REI. 6

6. 2 Solving Systems Using Substitution � 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

6. 3 Solving Systems Using Elimination � � � 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

6. 3 Solving Systems Using Elimination � 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

6. 4 Applications of Linear Systems � � � 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

6. 4 Applications of Linear Systems � 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.

6. 5 Linear Inequalities � � � 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

6. 5 Linear Inequalities � � 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

6. 6 Systems of Linear Inequalities � � � Pg. 400 – 405 Obj: Learn how to solve systems of linear inequalities by graphing and to model realworld situations using systems of linear inequalities. Content Standard: A. REI. 12

6. 6 Systems of Linear Inequalities � � � 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