Solving Special Systems

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Solving Special Systems

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Presentation transcript:

Solving Special Systems Essential Question? How can you solve a system with no solution or infinitely many solutions? 8.EE.8b

Common Core Standard: 8.EE.8 ─ Analyze and solve pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Objective - To solve special systems of linear equations and to identify the number of solutions a system of linear equations may have.

3 Possible Outcomes 1) 2) 3) Lines Intersect Lines Parallel Lines Coincide (Overlap) One Solution No Solution Infinitely Many Solutions Consistent & Independent Inconsistent Consistent & Dependent

Infinitely Many Solutions

Solve the system graphically, by substitution, and by elimination. Graphic Method

Solve the system graphically, by substitution, and by elimination. Substitution

Solve the system graphically, by substitution, and by elimination. Elimination

Solve the system graphically, by substitution, and by elimination. Graphic Method No Solution

Solve the system. Substitution False! Not true. No Solution

Solve the system. Elimination False! Not true. No Solution

Solve the system any way you choose. Elimination TRUE! They are Identical Infinite Solutions