Chapter 6.1 Common Core – A.REI.6 Solve systems of linear equations exactly and approximately, focusing on pairs of liner equations in two variables.

Objectives – To solve systems of equations by graphing. To analyze special systems.

Ch 6.1 Notes Solving two equations two unknowns by Graphing

One Solution Infinitely Solutions No Solution(They Cross) (Same Line) (Parallel Lines)

Chapter 6.2

Common Core – A.REI.6 Solve systems of linear equations exactly and approximately, focusing on pairs of liner equations in two variables.

Objectives – To solve systems of equations by using substitution.

Ch 6.2 Notes

Solving two equations two unknowns by Substitution1) Take an equation and either solve for X or Y2) Plug it into the other equation and solve.3) Substitute it back into the original equation to

solve for the other variable.Solve y = 3x x + y = -32

Chapter 6.3

Common Core – A.REI.5 & A.REI.6 Prove that, given…two equations…replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Objectives – To solve systems by adding or subtracting to eliminate a variable.

Ch 6.3 Notes

Solving two equations two unknowns by Elimination

1) Eliminate the X or Y variable by making them opposites of each other and then add the two equations up.

2) Substitute the answer into either equation to solve for the other variable.

Solve 2x + 5y = 17 6x – 5y = -9

Solve 5x – 6y = -32 -3x – 6y = -48

Solve -2x + 15y = -32 7x - 5y = 17

Solve 3x + 2y= 1 4x + 3y = -2

Chapter 6.4

Common Core – A.REI.6 Solve systems of linear equations exactly and approximately, focusing on pairs of liner equations in two variables.

Objectives – To choose the best method for solving a system of linear equations.

Ch 6.4 Notes

Applications of Linear SystemsFinding a Break Even PointA Fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50. The designer spends $1400 on advertising. How many hats must the designer sell to break even?

Identifying Constraints and Viable SolutionsThe local zoo is filling two water tanks for the elephant exhibit. One water tank contains 50 gal. of water and is filled at a constant rate of 10 gal/h. The second water tank contains 29 gal of water and is filled at a constant rate of 3 gal/h. When will the two tanks have the same amount of water?

Solving a Wind or Current ProblemPlane A flies from Charlotte, North Carolina, to Los Angeles, California at a rate of 495 mi/h with a headwind. At the same time, Plane B flies form Los Angeles to Charlotte at a rate of 550 mi/h with a tailwind. The air speed of each plane is the same. The ground speeds are shown below. What is the air speed? What is the wind speed?

Chapter 6.5 and 6.6Common Core – A.REI.12 & A.CED.3 Graph the solutions to a linear inequality in two variables as a half-plane.

Objectives – To graph linear inequalities in two variables. To use linear inequalities when modeling real-world situations. To solve systems of linear inequalities by graphing. To model real-world situations using systems of linear inequalities.

Ch 6.5 and 6.6 NotesGraphing Linear Inequalities

1) Graph the lines< or > use a dotted line< or > use a solid line

2) Shade above or below, or left or right of the line by picking a point and seeing if it works in the inequality.