# 4-5 reteaching writing a function rule answers to logo

Swedish Date Writing Day Month Year Why do Americans write the month Use international date format writing the date in full letters would be better than the example above. YYYY is the year [all the digits. Solve systems of linear equations by graphing. Solve systems of linear equations by elimination. Solve applications of linear systems. Mental Math Find the additive inverse of each expression y y 3. The goal of linear programming is to help business owners make decisions that will not violate any constraints and achieve improvement in productivity.

Even though business owners have a limited number of constraints, linear programming software has the capability to optimize results that contain an infinite number of variables and constraints.

In this chapter, students will learn about solving systems of equations and inequalities. Equations and inequalities are often used to model real-life situations. Students should become familiar with solving and graphing systems of equations in two and three variables, and systems of inequalities in two variables.

Students will also become familiar with linear programming. Point out to students that they may need to solve the equation for y before graphing. Students should expand each table until a common point is found. Emphasize that an infinite number of points satisfies each of the individual equations given, but at most, only one point satisfies both equations.

Ask students to recall other types of equations they have graphed, such as quadratic equations or absolute value equations. Ask students to visualize how many solutions a system of two quadratic equations can have. There may be 0, 1, 2, 3, 4, or infinitely many solutions. Strategy Cooperating Ask students to work in pairs. Have each student write one linear equation. Students should then graph both equations and find the solution to the system of equations. Many student pairs of equations will not result in integer solutions.

Discuss why many of the solutions were not integers. Challenge students to write a system of equations that has integral solutions. Answer to Critical Thinking A set of perpendicular lines is an independent system because the graphs of the lines intersect at one point.

Parallel lines have the same slope, but different y intercepts. Coinciding lines have the same slope and the same y intercept.

Intersecting lines have a different slope and may or may not have the same y-intercept. The y-intercept of both lines is 6. Therefore, the lines are coincident. The slope of the second line is 3. The y-intercept of both lines is 8. The first system should be dependent, the second system should be inconsistent, and the third system should have a solution of 3, 1.

Ask students to share their systems of equations as well as their strategies for writing each system.Przewodnik Tapicerski - tkaniny tapicerskie, materiały tapicerskie, akcesoria tapicerskie, poradnik tapicerski the court did not rule on the constitutionality of requiring proof of U.S.

citizenship to register to vote. If a resident chose to register to vote using the Arizona form – which requires proof – rather than the federal form. Practice Tests and Answer Keys Practice Test Answer Key © National Restaurant Association Educational Foundation. 