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3:1 Solving Systems of Equations by Graphing

3:1 Solving Systems of Equations by Graphing. To solve systems of equations by graphing To determine whether a system of linear equations is consistent and independent, consistent and dependent or inconsistent. Warm-up: Type 1 writing. 3 lines or more – 2 minutes

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3:1 Solving Systems of Equations by Graphing

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  1. 3:1 Solving Systems of Equations by Graphing • To solve systems of equations by graphing • To determine whether a system of linear equations is consistent and independent, consistent and dependent or inconsistent

  2. Warm-up: Type 1 writing 3 linesor more – 2 minutes In purchasing a cell phone, you could either pay $50/month + .02/text or $40/month + .04/text. How do you know which plan to choose? 30 seconds Finish your thought.

  3. System of equations: A set of two or more equations that contain the same variables

  4. Lesson 1 Contents Example 1Solve by Graphing Example 2Break-Even Point Analysis Example 3Intersecting Lines Example 4Same Line Example 5Parallel Lines

  5. Solve the system of equations by graphing. Example 1-1a Write each equation in slope-intercept form. The graphs appear to intersect at (4, 2).

  6. Original equations Replace x with 4and y with 2. Simplify. Example 1-1a Check Substitute the coordinates into each equation. Answer: The solution of the system is (4, 2).

  7. Solve the system of equations by graphing. Example 1-1b Answer:(4, 1)

  8. Break-even point: In business applications, the point at which the income equals the cost

  9. Let Cost of books is cost per book plus set-up charge. y = 2x + 200 Example 1-2a Fund-raisingA service club is selling copies of their holiday cookbook to raise funds for a project. The printer’s set-up charge is $200, and each book costs $2 to print. The cookbooks will sell for $6 each. How many cookbooks must the members sell before they make a profit?

  10. Income from books price per book number of books. is times y = 6 x Example 1-2a Answer: The graphsintersect at (50, 300). This is the break-evenpoint. If the groupsells less than 50 books, they will lose money.If the groupsellsmore than 50 books, they will make aprofit.

  11. Example 1-2b The student government is selling candy bars. It cost $1 for each candy bar plus a $60 set-up fee. The group will sell the candy bars for $2.50 each. How many do they need to sell to break even? Answer:40 candy bars

  12. Evaluate f(-4) for f(x) =│2x + 6│ • 14 • -2 • 4 • 12 • 2

  13. Name that function • Step • Constant • Absolute Value • Round Down

  14. Name that function • Step • Constant • Absolute Value • Piecewise

  15. Consistent: A system of equations that has at least one solution Inconsistent: A system of equations that has no solution (parallel lines)

  16. Independent: A system of equations that has exactly one solution (intersecting lines) Dependent: A system of equations that has an infinite number of solutions (same line)

  17. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-3a Write each equation in slope-intercept form.

  18. Example 1-3a Answer: The graphsof the equationsintersect at (2, –3). Since there is one solutionto this system, thissystem is consistentand independent.

  19. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-3b Answer: consistent and independent

  20. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-4a Since the equations are equivalent, their graphs are the same line.

  21. Example 1-4a Answer: Any ordered pair representing a point on that line will satisfy both equations. So, there are infinitely many solutions. This system is consistent and dependent.

  22. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-4b Answer: consistent and dependent

  23. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-5a Answer: The lines do not intersect. Their graphs are parallel lines. So, there are no solutions that satisfy both equations. This system is inconsistent.

  24. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Example 1-5b Answer: inconsistent

  25. End of Lesson 1

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