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

2. 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.

3. 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.

4. 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?????

5. 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

6. 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)

7. 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!

8. 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…

9. 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.