Linear Systems CH. 3.1 SOLVING SYSTEMS USING GRAPHS EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

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Presentation transcript:

Linear Systems CH. 3.1 SOLVING SYSTEMS USING GRAPHS EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Bell Work Evaluate 1. 9t + 6(2v-t) -7v; t=1, v=5 Write in slope-intercept form 2. y-5x = 16 Graph each equation y = 3x EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving Systems using graphs Linear systems of two equations can be analyzed using the nature of the solutions. One solution  2 lines intersect at one point  The slopes of the lines are not equal  The y-intersects may or may not be equal Infinitely many solutions  2 lines coincide  The slopes are equal  The y-intersects are equal No solution  2 parallel lines  Same slope, different y-intercept EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving a system by graphing EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Stop and talk…  What is a system of linear equations?  What does it mean for a system to have one solution?  Two solutions?  No solutions?  Describe one way that can always be used to solve a system of linear equations.  When solving a system, what is your ultimate objective? EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving a system by graphing EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving a system by graphing Now you try… EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Concept Summary EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving a system by graphing Y = 2x +1 -4x + 2y = 2 What is the solution(s)? EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Solving a system by graphing Now you try… Y = 1/4x /4x + y = 6 What is the solution(s)? EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Classifying a system without graphing EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Classifying a system without graphing Now you try… EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.

Closure (On your bell sheet) In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent? Explain. EQ: How can I solve a system using tables and graphs? I will solve a system using tables and graphs.