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Published byIra Merritt Modified over 6 years ago

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The equations you have been waiting for have finally arrived! 7.5 Special Types of Linear Systems

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43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will write, solve and graph systems of equations and inequalities. - Solve systems of linear equations graphically, with substitution and with elimination method. - Solve systems that have no solutions or many solutions and understand what those solutions mean. - Find where linear and quadratic functions intersect. - Use systems of equations or inequalities to solve real world problems. The student will be able to: - Solve a system graphically. - With help the student will be able to solve a system algebraically. With help from the teacher, the student has partial success with solving a system of linear equations and inequalities. Even with help, the student has no success understanding the concept of systems of equations. Focus 5 Learning Goal – (HS.A-CED.A.3, HS.A-REI.C.5, HS.A-REI.C.6, HS.A- REI.D.11, HS.A-REI.D.12): Students will write, solve and graph linear systems of equations and inequalities.

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Special linear systems Intersecting Parallel Same line One solution No solutionMany solutions (x, y) 0 = 2 0 = 0 When you solve each system, you either get an ordered pair, a false statement, or both sides are equal.

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Solve by substitution or combination then graph to check. 3x – 2y = 3 -6x + 4y = -6 Multiply the top equations by 2 6x – 4y = 6 -6x + 4y = -6 0 = 0 (true) What does this mean?????

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Rewrite in slope-intercept form: y = mx + b 3x – 2y = 3 -6x + 4y = -6 y = 3/2x -3/2 You have the same equations, so you have the same line and infinite solutions! You can graph to check. Infinite solutions Same line

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False Statement Parallel lines 3x – 2y = 12 -6x + 4y = -12 Solve by substitution or combination then graph. Multiply top by 2 6x - 4y = 24 -6x + 4y = -12 0 = 12 (False)

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Rewrite in slope-intercept form: 3x – 2y = 12 -6x + 4y = -12 y = 3/2x -6 y = 3/2x -3 Notice, same slope but different y- intercepts. You have parallel lines with NO solution. They will never intersect!

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Find a linear system for the graphical model. If only one line is shown, find two different equations for the line. a: y = 3 / 2 x + 1 b: y = 3 / 2 x - 1 y = 2x - 4 6x – 3y = 12 or 12x – 6y = 24 or 18x – 9y = 36 or…

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One More Time! Special linear systems: Intersecting Parallel Same line One solutionNo solutionMany solutions (x, y) 0 = 2 0 = 0 When you solve each system, you either get an ordered pair, a false statement, or both sides are equal.

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