<p> Algebra 1: Lesson Plan 12/1-12/2 – Systems of Linear Equations</p><p>Objectives 1. Students will understand that most pairs of straight lines will intersect at one point. 2. Students will understand how to graph two lines to find that point of intersection. 3. Students will understand how to check their work. </p><p>Essential Question 1. What are the advantages and disadvantages of solving a system of linear equations graphically versus algebraically? 2. How many solutions can a system of linear equations have? </p><p>Bell Ringer http://www.heymath.com/main/samples/us19/teacherstemplate.html ADD ON at bottom: How did you find your answer? Could these represent linear equations? </p><p>Introduction Hand out assignment worksheet Choose 4 students to help with a presentation. Have two students stand at corner of room, adjacent to each other, each holding the end of a piece of yarn. Two other students holding the other ends walk to the opposite corner of the room. Stretching the yarn as they go. </p><p>Have students record observations about the lines/intersections on their worksheet. Review ideas of line vs. line segment. Have the students imagine the lines go on forever in both directions. Would there be multiple intersections? </p><p>Cooperative Assignment Tasks will be displayed on the board one at a time. Students will work in pairs to complete each task. Students will write the equation given on their worksheet, and then complete the instructions. Students should all write their work on paper and white board, even though they are working in pairs. </p><p>Task 1, Part 1: Graph the equation x + y = 5. 2 minutes will be given. At that time, students will be given part 2 to the task. </p><p>Task 1, Part 2: Graph the equation y= 2x – 1 on the same graph as Part 1. 2 minutes will be given. At that time, students will be given part 3 of the task. </p><p>Task 1, Part 3: Determine where the two graphs intersect. Write the solution as an (x, y) coordinate. Then check your answer by plugging that point into both equations. Write answer on worksheet and show your answer and check work on the white board. 3 minutes will be given. At that time, students should have their answer, and check work shown both on their assignment page and on their whiteboard Public Record of each part of task 1 (graphing each line, finding the solution, checking answer)</p><p>Explain to students that this is called a System of Linear Equations and what a problem/question would look like. Explain that the solution to a system of equations in the ordered pair that represents the point of intersection (where the lines both share the same ordered pair). </p><p>Repeat the activity 3 more times with the following sets: Task 2, Part 1: y = 2x + 3 Task 2, Part 2: y = -2x – 5 Task 2, Part 3: (-2, -1)</p><p>Task 3, Part 1: y = 4x + 3 Task 3, Part 2: x + y = 8 Task 3, Part 3: (1, 7) </p><p>Task 4, Part 1: y = 2x + 3 Task 4, Part 2: 2y = 6x + 4 Task 4, Part 3: (1, 5)</p><p>Use accountable talk, public record, and popcorn answering with whiteboards for each task. </p><p>Extension What if you had y = 3x + 4 and y = 3x +6? What does the line look like? Is there a point of intersection? How many solutions would there be?(no solution) </p><p>*Parallel Lines = No solution*</p><p>What if you had y = 2x + 1 and -4x + 2y = 2? What does the line look like? Is there a point of intersection? How many solutions would there be? (infinite solutions)</p><p>*The Same Line = Infinite Solutions*</p><p>Closing Have students summarize in their notes what they know about systems of linear equations, while summarizing on a public record. Possible Points to Include: ~ The point of intersection of two lines is the solution for the two equations ~ Can write in slope-intercept form to graph the to lines ~ Can check solution by plugging it into both equations ~ Parallel Lines (identical slopes) have No Solution because there is no intersection ~ Equations that graph the same/identical line have infinite solutions Name: ______Algebra 1: Systems of Linear Equations – Worksheet 1 Introduction Record your observations about the human line graphing here:</p><p>______</p><p>______</p><p>______</p><p>______</p><p>______</p><p>Task 1 Equation – Part 1: ______Equation – Part 2: ______</p><p>Solution – Part 3: ______Check: ______Task 2 Equation – Part 1: ______Equation – Part 2: ______</p><p>Solution – Part 3: ______Check: ______</p><p>Task 3 Equation – Part 1: ______Equation – Part 2: ______</p><p>Solution – Part 3: ______Check: ______Task 4 Equation – Part 1: ______Equation – Part 2: ______</p><p>Solution – Part 3: ______Check: ______</p><p>Extension Equations: ______and ______(graph these equations on the first graph) Solution: ______Why? ______Equations: ______and ______(graph these equations on the second graph) Solution: ______Why? ______Name: ANSWER KEY Algebra 1: Systems of Linear Equations – Worksheet 1 Introduction Record your observations about the human line graphing here:</p><p>Possible Observations: Four people graphed two straight lines. The lines could be never ending. The lines were going opposite directions. The lines intersected at one point. If the lines continued, they would never intersect again. That one point is the only ordered pair that the lines would share. </p><p>Task 1 Equation – Part 1: x + y = 5 Equation – Part 2: y= 2x – 1</p><p>Solution – Part 3: (2, 3) Check: 2 + 3 = 5 and 3 = 2 (2) - 1 Task 2 Equation – Part 1: y = 2x + 3 Equation – Part 2: y = -2x – 5</p><p>Solution – Part 3: (-2, -1) Check: -1 = 2(-2) + 3 and -1 = -2(-2) - 5</p><p>Task 3 Equation – Part 1: y = 4x + 3 Equation – Part 2: x + y = 8</p><p>Solution – Part 3: (1, 7) Check: 7 = 4(1) + 3 and 1 + 7 = 8 Task 4 Equation – Part 1: y = 2x + 3 Equation – Part 2: 2y = 6x + 4</p><p>Solution – Part 3: (1, 5) Check: 5 = 2(1) + 3 and 2(5) = 6(1) + 4</p><p>Extension Equations: y = 3x + 4 and y = 3x +6 (graph these equations on the first graph) Solution: No Solution Why? They are parallel lines. They don’t intersect. They don’t share ordered pairs. </p><p>Equations: y = 2x + 1 and -4x + 2y = 2 (graph these equations on the second graph) Solution: Infinite Solutions Why? They are the same line. They share all of the same ordered pairs. </p>