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Linear Systems CH. 3.1

SOLVING SYSTEMS USING 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

3. 12+2y = 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-interceptEQ: 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…

1.

2.

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.

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 + 3

-1/4x + y = 6

What is the solution(s)?

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.