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)