Missy McCarthy Okemos High School

SOLVING SYSTEMS USING GRAPHING

LEARNING TARGETS

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

Solve a system of linear equations by graphing. Interpret the results.

WHAT IS A LINEAR SYSTEM?

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

Two or more linear equations together form a system of linear equations.

SOLUTIONS TO A LINEAR SYSTEM

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

Any ordered pair (values for the variables) that makes ALL of the equations true is a SOLUTION of the system.

EXAMPLE: SOLVING BY GRAPHING

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

One way to find the solutions of a linear system is by graphing the equations in the system to find the point that they have in common.

Find the solution to the system of equations by graphing.

y = 2x – 3y = x - 1

EXAMPLE: SOLVING BY GRAPHING

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

Find the solution to the system of equations by graphing.

3x + 4y = 122x + 4y = 8

EXAMPLE: APPLICATION

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

I’m planning to take a Zumba class at Court One. I called to find out the costs and was told that it is $4 per class for non-members while members pay a $10 fee and an additional $2 per class. Write a system of equations to model the cost for non-members and members and solve by graphing. Interpret your solution.

SYSTEMS WITH NO SOLUTION

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

SYSTEMS WITH MANY SOLUTIONS

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

SUMMARY

What you will learn

What is a linear system?

Solutions to a linear system

Example: Solving by graphing

Example: Application

Systems with no solution

Systems with infinitely many solutions

Summary

Lines that intersect at one point have only one solution. These lines have different slopes.

Lines that are parallel have no solution. These lines have the same slope and a different y-intercept.

Lines that coincide/one lies right on top of the other have infinitely many solutions. These lines have the same slope and the same y-intercept.