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### 6.4B Elimination Using Multiplication

 Standard(s):A.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.A.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with grap), focusing on pairs of linear equations in two variables.I can use function notation to show that when f(x)=y and g(x)=y that f(x)=g(x).Essential Question:In what ways can the problem be solved, and why should one method be chosen over another?Learning Target:I can define systems of equations.(Knowledge)I can solve a system of two equations in two variables by elimination.(Application)I can define solutions of systems of equations.(Knowledge)I can explain why some linear systems have no solutions.(Comprehension)I can identify linear systems with no solutions.(Comprehension)I can explain why some linear systems have infinite solutions.(Comprehension)I can identify linear systems with infinite solutions.(Comprehension)I can solve a system of linear equations algebraically to find an exact solution.(Application)I can find an exact solution to a system of linear equation by graphing.(Knowledge)I can explain that a point of intersection on the graph of a system of equations is the solution to both equations.(Comprehension) I can use function notation to show that when f(x)=y and g(x)=y that f(x)=g(x).(Application)I can explain that the value making f(x)=g(x) true is the x coordinate of the intersection point.(Comprehension)Warm-Up:     Notes: Refer to the notes from section 6.4AActivity: Click on the image below for an activityExtra Help:Click on the image below for help Assessment/Homework:Worksheet 6.4 2-14 even,15