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Systems of Equations and Inequalities

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.

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Systems of Equations and Inequalities

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  1. Systems of Equations and Inequalities Chapter 6

  2. 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

  3. 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)

  4. 6.1 Solving Systems by Graphing • Inconsistent – a system of equations that has no solution (parallel lines)

  5. 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. 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

  7. 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

  8. 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

  9. 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

  10. 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.

  11. 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

  12. 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

  13. 6.6 Systems of Linear Inequalities • 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

  14. 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

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