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6-1 Solving systems by graphing

This lesson focuses on how to solve systems of linear equations using graphing. Students will learn about the different types of solutions: a single intersection point, parallel lines with no solution, and identical lines with infinite solutions. Through examples, students will practice graphing equations and identifying their intersections, gaining a solid understanding of how systems work. Additionally, real-world applications, such as decision-making for cable subscription costs, illustrate the relevance of these concepts. Students will apply their knowledge in homework exercises.

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6-1 Solving systems by graphing

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  1. 6-1 Solving systems by graphing Miss battaglia – algebra 1 cp Objective: solve systems of linear equations by graphing.

  2. Warm up Find roads that intersect once, more than once, and never intersect. Describe the roads as intersecting lines, curves, or parallel lines.

  3. Think & discuss • How can you show all the solutions of the linear equation y = 2x – 3? • Two or more linear equations together form a system of linear equations. One way to solve a system of linear equations is by graphing. Any point common to all the lines is a solution of the system.

  4. Solve the system of linear equations by graphing • y = 2x – 3 • y = x – 1 Check your answer!

  5. Solve the system of linear equations by graphing • y = x + 5 • y = -4x Check your answer!

  6. Solving special types of systems • A system of linear equations has no solutionwhen the graphs of the equations are parallel. There are no points of intersection, so there is no solution. • A system of linear equations has infinitely many solutionswhen the graphs of the equations are the same line. All points on the line are solutions of the system

  7. Solve by graphing • 4y = 4 + x • x + y = -1

  8. Solve by graphing • y = x • y = x + 6

  9. Solve by graphing • 2x + 2y = 1 • y = -x +

  10. Solve by graphing • x = 1 • x = -2

  11. entertainment • A cable company offers a “pay-per-view” club. Let c = the annual cost and n = the number of movies you watch in a year. Write a system of linear equations to decide whether to join the club.

  12. homework • Pg272 # 1 – 10

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