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Solving Systems using graphing

Solving Systems using graphing. Missy McCarthy Okemos High School. 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.

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Solving Systems using graphing

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  1. Solving Systems using graphing Missy McCarthy Okemos High School

  2. 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.

  3. 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.

  4. 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.

  5. 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 – 3 y = x - 1

  6. 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 = 12 2x + 4y = 8

  7. 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.

  8. 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

  9. 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

  10. 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 coincide/one lies right on top of the other have infinitely many solutions. These lines have the same slope and the same y-intercept. Lines that are parallel have no solution. These lines have the same slope and a different y-intercept.

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